Well, I'm of the mind that the multiplayer is completely unnecessary in a game such a Batman, though the take on it does seem different to the norm. The biggest problem is that for the first 6 weeks after the games release, the lobbies tend to see fairly brisk activity, but then what usually happens is that people who attack the multiplayer having finished the campaign, stick with it for a few days, and then drift off to something else at which point the lobbies become a desolate place to be.
The batman games, for me, are far better that the likes of CoD and Battlefield, but Batman will not sell in the same quantities as those games, and so the lobbies will never see as much traffic. It really is a case of it being pretty pointless in the long run. And even though they say two different teams are making the two components (campaign and multiplayer) to effectively stave of the criticism of the fans that more levels could be produced for the campaign, it is still the case that there is a finite pot of money to be spent on making the game and so money that could be used to make more levels is instead going into the multiplayer. Maybe they will go the Bioshock route, and drop the multiplayer for number 4 if the take up is not sufficient.