I believe if you get the latest Quake3 download from id you'll also get the Q3DedicatedServer command-line executable. It doesn't require a connection to the Window Server, so you can run it without having a user logged in on the console if you wish.
Other Quake3-based games may respect the command-line argument "+set dedicated 1", but it depends on the implementation of the Mac port. (I'm not sure how one would provide the command-line args to a CFM-based executable.) That argument should cause it to load without trying to go into fullscreen OpenGL, but it'll still want to launch within a WindowServer session. Again, though, it depends on the port -- I'm pretty sure JK2 and SoF2 work this way, but I dunno about Wolf, MoHAA, or Elite Force.