There is absolutely no parent who's problem is a child who thinks "I need to eat right now".
That doesn't mean my toddler wouldn't prefer ice cream over whatever is for dinner, though.
I only mention it because, as any parent knows, infants are effectively small finite state machines, and you can deal with their crying even half-awake, if you go through a mental checklist. But you'd better not miss a state to check :).
So yeah, good fucking luck if that happens. You'll have to feed on a schedule, change regularly and check even more regularly, guess appropriate temperature etc because the baby will be screaming bloody murder if awake no matter what.
My son during teething was hungry a lot. He was absolutely unwilling to eat for hours till we found whichever thing he was going to tolerate each time (since he's stopped teething for now he's gotten a lot better about it, but you still have to offer food since he doesn't always recognise he is getting hungry).