I'm pretty much certain that standard issue p2p approaches will not work on mobile without a rethink, but I do think its possible.
SnapChat may not be the best example, since it's a very ephemeral quick and as you say asynchronous app. A better use case would be something with a more prolonged engagement like a game, video conferencing, telepresence, etc. Those also have significantly higher bandwidth requirements that would make something like that more interesting.
Also sounds like if it can be done on iOS, it can be done anywhere, so if one were going to take a do the hard stuff first approach one should start with iOS.