There is no standalone server for the consoles. I fought to try and get something put together were we could host remote servers, or for them to have something hosted on the Sony/Microsoft network but it was a no-go. I even offered to work on writing the code for it myself, but couldn't get approval to do so. TellTale just wouldn't bend at all. Which was really sad, because I had IG interested in it at least a little bit.
It would have been great too, because with remotely-hosted servers for the players to rent or set up, the console could be opened up to 8-player co-op this way. Sadly this was not able to happen.