I never said "click the minimize button".
It was a logical assumption from your "you should be able to minimise mIRC".
And no, I don't get any response from mIRC during the time when your 'testcase' alias or '//while (1) noop' is running, regardless whether or not I keep mIRC as the active app, or whether I switch to another process by clicking on the other icon in the taskbar or using Alt+Tab. It won't respond to the minimize/close buttons in the upper right corner, it won't respond to closing from the taskbar, either from the red X in the taskbar popup window or rightclicking the taskbar to get the 'close window' choice to appear. The closest thing I can get to a response during the infinity loop is that the taskbar does let me toggle the "pin this program to taskbar" setting.
When I switch to another process, the display switches to that process. When I click on the taskbar or use Alt-Tab to switch back to mIRC, there's no visual feedback of the process switching back until I press Control+Break. Only then does the display change from the other app's contents back to displaying the mIRC window.