Yeah you could do things like set timer interrupts, and starting in somewhere like MacOS 8.6 there was an actual multitasking (and multi-CPU) nanokernel running beneath everything that allowed you to schedule tasks in a more modern way.

But those tended to have some pretty gnarly limitations (like I think in interrupts you can't allocate memory) so AFAIK they were only used for stuff like real-time audio, I dunno if anyone ever used those to do screen drawing, so in practice I can't think of anything that would interfere with menu drawing.