For some strange reason, games run in text mode on windows machines use *more* resources than games run in windows and minimized. At least in 3.06 this was the case.
I use remote desktop whenever I'm playing from my laptop, out of fear that IP address clashes will trigger the copy protection.
If you are both playing in *and* hosting a game, RDC sometimes crashes the dom3 executable, at least on my machine. Of course, my machine is overclocked and not as stable as might be desired
Other than that, it appears to me that you can minimize a GUI session, log on from RDC, and then log in again and again from different machines without killing the game.
If you actually log out that might kill it, I've never tried it. But you can certainly administer a server by RDC.
Disclaimer: I am durnk.