Some may; in fact, it's quite probable at this point. But the Pokédex implies that it's the case for them all, and yet they can be bred by anyone with a compatible partner. Barring some terrifying implications about the local afterlife, those should be human soul-free. Though there's always the possibility that they were merely exaggerating slightly...

A few of us have been here about that long, yes, but I can hardly use my own health as a guideline. My lifestyle is extremely different from the one I have at home, and I've been eating fresh Blissey eggs daily for over half that time.