I was paranoid about this before the birth and spent a good part of the day in labour shuffling to the toilet in my flip flops.
I did a huge poo during initial labour and can remember trying to wipe my bum with big wadges of toilet roll in between the bloody contractions which was very difficult. I also couldn't reach round my back very effectively as I fell down our stairs on my back a few days before.
So more likely that when I climbed back on the table the midwife had to stare at a load of chewed up bog roll stuck up my behind. 
I do remember trying to clench my bum hole in a ladylike way whilst pushing out a 10 lb baby and that effort was overwhelming so I just gave up and pushed very pore and orifice available.
DH would still be ribbing me senseless if I had done a poo so I think I got away with that one. I'm sure with the size of my son there was no room anyway!
The scary thing was the next morning doing a poo and having to push with 14 stitches up my fanjo - terrifying!