It doesn't mean he gets his soul back at all - if the Horcrux is destroyed, it could well be that the soul part is destroyed. Which means that V. won't notice since he's lived without it so long.

I think of it as being essential caches of something that he needs to go on living - but in many ways, V. is essentially soulless in terms of our understanding of what a soul is, but the soul is something that can keep him going.