I personally don't think you'd even be able to sleep as your babies poop will smell up the room.
I'd personally wake the baby up and change them. If your baby gets diaper rash from sleeping in the poopy diaper then you certainly won't be getting much sleep then either as your baby will be crying because of the painful diaper rash.
Even if it takes a little bit for your baby to fall back to sleep after waking him/her up it's best to go ahead and change the poopy diaper.
Wet diapers aren't as bad to let your baby sleep through but poop contains bacteria that shouldn't stay near your babies skin for too long.