I think that's a really, really good idea. And you could have a health bar and some sort of attack/defense system... I think this should only be used for groups, so you'd have group battles, and group members get a conformation page asking if they want to be in the battle or something.
Like I said, once the battle started, you could start attacking by swiping, kicking, biting, tackling, etc., and you could growl/hiss/snarl, and that would reduce attack or defense. [Oh, god, pokemon...] Buuut unlike pokemon, it isn't turn-based, and you and you can move around freely.
But once your health bar ran out, you were out of the battle. You would just have to watch, or you would be redirected or something. xD Whenever all of your members are out of the battle, that means that the other side has won.
But I can see how that'd be abused. One side would just get a bunch of members and outnumber the other side somehow. I can really, really see a bunch of mean noobs doing that. But maybe an even-matchup thing can be implemented? Like, if one group has five people battling, the other group would have to have 4-6 people battling on their side?
This way, there aren't any powerplayers claiming to win by biting off your head in the chat! It's completely fair, and they can baaaww all they want when they've lost, but that's what happened, fair and square.*cough*
I wish this could happen, it would be so epic... *w*