Possibly, but not entirely certain, but if they're "night time" spawns, they despawn during the day when out of render distance. This is what made taming 2* wolves such a pain. You'd have to tame the pets, let them breed, and the babies will be permanent, but the original 2 would disappear once out of render range. So you have to baby sit them until you have your babies, and even still I'd probably baby sit them until they're adult just to be safe.
I could be entirely wrong though.