No. In general, JBossAS performs about the same on Windows as on Linux on the same hardware. At work, some of my coworkers have done extensive performance testing with JBossAS on both Linux and Windows, using industry benchamrks, and the results have been the same.
That is not to say that you might not notice differences in some areas. For example, on my desktop it takes 1/2 the time startup JBossAS on Ubuntu as on XP. Same hardware, same level of JDK. But if I use JMeter to test the performance of a web app, I get very similar results regardless of the OS.
And whether or not you run a full-featured GUI on Linux has no bearing on the matter.