On a second monitor (with no taskbar), a maximized window would be virtually the same as a "full screen" application, no? Are you using mIRC in the window with or without the taskbar? In the latter case, you should already have the ability to have mirc running "full screen" (you can already hide the toolbar and menubar), and unless your problem is really with the titlebar this should be fine-- note the titlebar is used to show channel topics, so some form of bar would still need to exist at the top of the window even if it was not the window titlebar... I guess I just don't get what you get out of a full screen window.
Also note that if you're looking for a minimalist interface when the application is full screen (no titlebar, no toolbar, no menubar, no switchbar, no treebar) you can script this with custom windows.