Plugging in a router shouldn't be a problem if you plug the WAN port into the school network. However, if you plug one of the client-side ports into the school network, you'd have a problem :-)

Also, wireless in a dorm might be a problem, because you could actually run out of channels pretty easily. Given that the original concern was "other students connecting without recognizing it," then turning on WPA and/or turning off the announce beacon ought to solve that problem.