Well, seems I was a little hasty. Although the Toolset does open and work under Linux now, it does still have some issues, and will frequently throw Access Violation errors. However unlike Windows where this completely halts the application, on Linux you can just keep on working past them, with no ill effects as far as I can see. So, still far from working perfectly, but it does allow you to do some editing on a Linux box.
The Player and DM clients however do work extraordinarily well - in fact work better then the native Linux client! Better framerates, no sound bugs, and you can even switch Desktops with Cntl-Alt-Arrow. Extremely nice.