The doctors will hide it. If your really worried mention something to a nurse. "Im scared i might poop i dont want anyone to see that" and im sure they will tell u that they will cover it up.
I don't think so... I remember I was in the hospital and told them I needed to poop they said no cause it was just the baby pushing down!:o I ended up having csection so I don't know about pooping while giving birth! I'm going for a vbac and that's the thing I'm mostly scared of...POOPING WHILE HAVING MY BABY!!:'D