Yes, it leaves the menu open here :-) This issue is different to yours - I was only able to reproduce your issue once or twice and it required pressing the ALT+Tab key combination repeatedly and randomly many times. My guess is that both of the issues are related.
mIRC already checks to see if it is the active application when handling this feature.
Wine can vary from standard Windows behavior in some very subtle ways. In this case I performed low-level debugging to try to find a work around. mIRC was unable to detect the key presses, or any other events, that it needs to detect in order to make this feature work under Wine, so it does not look like there is a solution.