I used to fall asleep a lot and thought nobody noticed but everybody did. However I did once get asked a question while asleep, woke up, gave a full answer and even asked a follow up question, which shows you how much attention you actually needed to pay.
Nowadays my meetings are generally telecons so I can just move the window somewhere out of the way and do something else. I never have my camera on so I’ve been known to go out for a fag or to get coffee - on the very rare occasions somebody asks you something while you’re away you can always say “oh sorry someone came to my desk with an urgent question”. I have also heard people say “sorry I wasn’t listening could you repeat that?” when asked something.