It's going to happen. Especially since Bully is an open-world game, I'd imagine R* would want to take full advantage of that.
I'd expect the usual. The least we'll get is an online free roaming experience, and even able to have our own customizable characters. I think what they're going to do is basically make the singleplayer portion multiplayer, which might be what they're going to do with GTA V's online MP. Their calling it "Grand Theft Auto Online" which sounds pretty big.
And with competitive multiplayer, I'm not really sure how it would work, but it could.