It looks like this explanation for the origin of the Borg is not canon.

The Star Trek Encyclopedia speculates that there could be a connection between the Borg and V'ger, the vessel encountered in Star Trek: The Motion Picture; this is advanced in William Shatner's novel The Return. The connection was also suggested in a letter in Starlog #160 (November 1990). The letter writer, Christopher Haviland, also speculated that the original Borg drones were members of a race called "The Preservers", which Spock had suggested in the original series episode The Paradise Syndrome might be responsible for why so many humanoids populate the galaxy. Coincidentally, in the novelization of Star Trek: The Motion Picture (written by Gene Roddenberry), the V'ger entity notes that the Ilia probe is resisting the programming given to it because of residual memories and feelings for Decker, from its precise replication of the Deltan lieutenant. When V'ger becomes aware of this, it decides that "the resistance was futile, of course".

The extra section of the game Star Trek: Legacy contains the "Origin of the Borg", which tells the story of V'ger being sucked into a black hole. V'ger was found by a race of living machines which gave it a form suitable to fulfilling its simplistic programming. Unable to determine who its creator could be, the probe declared all carbon-based life an infestation of the creator's universe, leading to assimilation. From this, the Borg were created, as extensions of V'ger's purpose. Drones were made from those assimilated and merged into a collective consciousness. The Borg Queen was created out of the necessity for a single unifying voice. However, with thoughts and desires of her own, she was no longer bound to serve V'ger. This explanation, however, is not canon.

Unfortunate, because that would be kind of awesome.

V'ger was NOT the creator of the Borg, nor did the Borg have anything to do with V'ger, contrary to what is believed or written in the Star Trek lexicon to try to explain how the V'ger vessel was created. Here is why:

Fact #1: The Borg have been in existence since the mid 15th century.

Voyager 6 (V'ger) was created and launched into space in the late 20th century. The Borg were in existence long before NASA was created, 500 years or more. Even if the "black hole" had time warped Voyager 6 back 500 years in the wrong direction it was originally heading, the technology differences are massive. As to the origins of the Borg, no true information has made available except that the Vardwar confirm in Star Trek Voyager that the Borg have been in existence since at least the early 15th century by human time frame and Seven of Nine confirming that much of Borg history of that time was fragmented and lost. The whole Borg/V'ger idea/concept to try to explain the creation of the V'ger vessel, is just that - an idea, and unfortunately it's a false one that the Star Trek writers have been clinging to wrongly, to come up with some plausible explanation for the creation and early history of the Borg and of V'ger.

Fact #2: Voyager 6, had it ended up in Borg space, would have been seen as space junk at worst, a minor oddity at best.

The Borg would NOT waste massive amounts of resources creating a vessel so huge as the V'ger craft, just to watch it go bye bye without serving some useful purpose to the Borg. Knowing Borg mentality, Voyager 6 most likely would have been either destroyed or assimilated had it encountered the Borg.

Fact #3: Probably the most important information on V'ger.

Going by Star Trek spacial quadrant charts and information provided in Star Trek: The Motion Picture, V'ger ended up on the far side of the Beta Quadrant, not the Delta Quadrant. According to what was giving, the personnel on the Epsilon 9 station reported the Klingons attacking V'ger in quadrant L-14. This is deep in Klingon territory in the Beta Quadrant, on the lower left hand side of the known star charts. The Borg are in the Delta Quadrant, located on the upper right. After the attack, the female crew member reported it would be passing very close to the station. When the senior officer asked where it was heading, the ensign replied "on a direct course to Earth." Following that line of trajectory backwards from Earth to Epsilon 9 to quadrant L-14 then out of the Beta Quadrant. Since V'ger was going straight from point a to b to c, the obvious conclusion was that the V'ger vessel was coming from the far edges of the lower Beta Quadrant, NOT the Delta Quadrant. Now some may argue that the Borg have transwarp conduits all over the place, in most sectors of know space including the Alpha, Beta and Gamma Quadrants. However, it's highly doubtful the Borg would have a "machine planet" in the Beta quadrant without the Klingons knowing about it. We can see the Klingons acting like they had no idea what the V'ger vessel was or how to deal with it, and reacted in true "shoot first, shoot second, shoot some more, then ask questions" Klingon style.

Fact #4: The V'ger vessel, as shown, followed no know Borg design or type of craft known to be in use by the Borg.

The V'ger vessels power type used (plasma energy) is different and much more advanced then what the Borg use or did or ever have used. IF the Borg did make the V'ger vessel, then logically it likely would have followed a similar design type and energy usage, perhaps a class 5 tactical cube or a class 5 long range tactical sphere, but it didn't follow any type of geometric shape.

Fact#5: The Borg were not made aware of the Alpha quadrant or Earth until the mid 22nd century and did not start poking around the Alpha quadrant until the late 24th century.

(Star Trek: The Next Generation, "Q-who" (2365)/Star Trek: First Contact (2371)/Star Trek: Enterprise: "Regeneration" (2153)). Q started the whole Borg introduction to the Federation in 2365. Even before this time there were already signs the Borg were nosing around the Delta/Alpha Quadrant Federation and Romulan borders. After the Borg were made aware of the existence of humans, the time loop came full circle with Star Trek: First Contact and Star Trek: Enterprise, "Regeneration" . Voyager 6 was launched into space and presumed lost to a "black hole" a full 150 years prior to the Federation even being created.

Fact#6: V'ger communicated by ultra high speed RADIO waves to the USS Enterprise in Star Trek: The Motion Picture.

If it was Borg design, then V'ger would have used more modern types of communication, the Borg being too advanced to use that primitive form of communication and would never use it anyway. V'ger broke down everything into data storage patterns via plasma energy attacks (including Lt. Ilea). The Borg, as we all know, incorporate things through assimilation. The technology and vessel that V'ger was using was far superior to know Borg technology (except for the radio communication).

All information shown from Star Trek canon (books not withstanding) clearly supports that Voyager 6 emerged on the far side of the Beta Quadrant in deep space in the opposite direction from the Delta Quadrant and Borg space. While it is repeated that voyager 6 encountered a race of machine beings never before or since encountered, as of yet, the race of beings V'ger encountered clearly were NOT the Borg.

Let me see what I can recall from memory.

Voyager 6 amassed an amazing amount of information, and shortly afterwards, encountered a machine-based race which recognized (what they thought was named) VGer as one of its kind, repaired it as best they could, and build it a ship so it could get home.

It's made pretty clear that until Q send the enterprise to meet the Borg, they were unaware of our existence, which suggests that they had no information that VGer's data banks would have provided. The unnamed machine race surely knew where VGer came from, cause they sent it back.

Neat bit of guessing, but not sure how correct it is.

For me, the difference in technology between the quality of V'ger's work and that of the Borg is simply to great. If you look at the quality of the Ilia probe with the molicule sized processors. The Borg are crude and clumsy by comparison.

There are a couple of times, once in First Contact, the other with Lore, that even Data and Lore were more advanced technologically than most drones. So it would be like the president of Ferrari deciding he needs a performance car, so let's build a "Model T Roadster". There would be no reason to make the Borg so primitive compared to the Ilia probe.

I feel like it's probably a mixture between the technological and biological becoming one, from separate origins.

In Star Trek: Voyager, the Borg Queen told Captain Janeway (and eluded the same to Commander Data in First Contact) that the Borg had originally developed their obsession with perfection as entirely biological beings living in the Delta Quadrant. They used selective breeding and genetic engineering, to "perfect" their biological form. At some point after that, they began including cybernetic components to further perfect their form, in their eyes, but she doesn't say exactly when.

So you have a race of biological beings that have standardized themselves in form and function, who, at some point, began augmenting themselves with technology in an effort to further perfect their species.

Elsewhere in the galaxy, the NASA Voyager probe assimilated so much data that it became self-aware, and then began assimilating more and more technology in an effort to become the "perfect" artificial intelligence. V'ger had reached the limit of its potential as an entirely technological being. In order to continue its evolution toward perfection, V'ger would have to begin assimilating organic biology. V'ger assimilated Lieutenant Ilia (probably the first Borg Queen - I mean just look at her) and Decker (the first Borg drone to serve the first Queen). Then V'ger left the Sol System headed for parts unknown.

If V'ger ended up in the Delta Quadrant, seeking to add more biological specimens to assimilate in order to add to its own distinctiveness, and encountered a race with the same unyielding obsession in the early (biological) Borg - then the rest is self-exolanatory.

And, on Voyager's journey home from the Delta Quadrant, they encountered two wormholes that not only covered vast distances, but also spanned many years of time. So, if V'ger had gotten to the Delta Quadrant via a wormhole, then there's no telling "when" it may have arrived there in the Star Trek canonical timeline.