Well, I'd imagine that any pets that would come up would be treated as items.
I mean, already there's been the duck hat, where little ducks appear around the wearer, and there was that one Labtech with the mutated rabbit on his head.
Don't think they need to have them be elements in the battle system. After all, who'd want to face some uber-rich user along with their expensive monster? Wouldn't really be fair to those who don't spend all waking hours to get gold :p