The latter is possible, as long as you make sure you share it with your multiplayer counterpart. If you have a different configuration in terms of installed software, it ofcourse will fail as you are "sharing a computer" kinda. The only difference being that the computer has 2 screens, two hd's, two (four?) floppies, two joysticks, two mouses etc, all connected by a thin wire of TCP/IP
Strange, come to think of it, but true hehe ;p