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If a person casts a spell and it's deflected can it hit an unintended target and work as intended?

For example, if a wizard casts a spell at someone to turn them into a dog, and it's deflected and hits another person, will that person turn into a dog?

I know there's the example of Ron's broken wand with the slugs and the charms spells, but I attribute that to the wand just having bad aim by being broken and just casting in the wrong direction.

Please account for Voldemort's casting of the Avada Kedavra spell at Harry and it killing the horcrux inside of Harry. Clearly that was not the intended target for the spell.

It would appear so. There's a brief mention in HP5 of the shield charm reflecting spells. There's no specific indication whether their effects would have been changed by the interaction

He was improving so fast it was quite unnerving and when Harry taught
them the Shield Charm – a means of deflecting minor jinxes so that
they rebounded upon the attacker – only Hermione mastered the charm
faster than Neville.

Later in the same novel Malfoy Sr. deflects Bellatrix's stupefaction spell. It impacts a shelf and appears to have much the effect you'd expect;

A jet of red light had shot from the end of Bellatrix Lestrange’s
wand, but Malfoy had deflected it; his spell caused hers to hit the
shelf a foot to the left of Harry and several of the glass orbs there
shattered.

and in HP7, a stunning spell bounces off of a window, hitting an innocent bystander

Harry sent another Stunning Spell at the Death Eater with the twisted
face who had tied up Ron, but the spell missed, rebounded on the
window and hit the waitress, who collapsed in front of the door.

and Hermione's "Blasting Curse" bounces off of a wall and destroys Harry's wand.

‘Harry,’ Hermione whispered, so quietly he could hardly hear her. ‘I’m
so, so sorry. I think it was me. As we were leaving, you know, the
snake was coming for us, and so I cast a Blasting Curse, and it
rebounded everywhere, and it must have – must have hit –’ ‘It was an
accident,’ said Harry mechanically. He felt empty, stunned. ‘We’ll –
we’ll find a way to repair it.’

There is a quite explicit example of this in Chapter Eighteen of Goblet of Fire:

"Furnunculus!" Harry yelled.

"Densaugeo!" screamed Malfoy.

Jets of light shot from both wands, hit each other in midair, and ricocheted off at angles – Harry's hit Goyle in the face, and Malfoy's hit Hermione. Goyle bellowed and put his hands to his nose, where great ugly boils were springing up – Hermione, whimpering in panic, was clutching her mouth.

"Hermione!"

Ron had hurried forward to see what was wrong with her; Harry turned and saw Ron dragging Hermione's hand away from her face. It wasn't a pretty sight. Hermione's front teeth – already larger than average – were now growing at an alarming rate; she was looking more and more like a beaver as her teeth elongated, past her bottom lip, toward her chin – panic-stricken, she felt them and let out a terrified cry.

In this case Harry's spell and Malfoy's spell both hit unintended targets after bouncing off each other, and their effects do not seem to have been affected (Hermione's teeth increased in size, which is literally the translation of dens augeo, and Goyle erupted in furuncles).

The second AK that Voldemort sent at Harry did just that (well, actually, 3rd. Or even 5th depending on how you count).

In the final duel during the Battle of Hogwarts, Voldemort was killed by his own deflected AK.

Voldemort was dead, killed by his own rebounding curse, and Harry stood with two wands in his hand, staring down at his enemy's shell. (DH)