Do you mean having your computer being a "dedicated" server? Or, are you just going to host the game on your computer and play on your computer at the same time?
As for connecting multiple PCs on one internet connection, its possible. For my network, you could use a router and hook them up in this order: Internet -> Router -> All of your PCs Granted, there are other ways to do it. All of your PCs will have (1) external IP, but each PC will have its own unique IP on the LAN (i.e. externally, it could be 18.104.22.168 for all your PCs but inside the LAN, PC #1 could be 192.168.1.101 PC #2 could be 192.168.1.102 etc...)
*crimeny, just saw how long ago this topic was started, sorry about this*