You can, yes, as you're using basically the same muscles. But not everyone does. I didn't. I had a home birth so had her on my bedroom floor and there was no poop. But I did have a pretty good clear out (diarrhea) about 10 hours before as labour was starting, so I'm sure that helped.
But don't worry about it. You won't care and nor will you're doctor or midwife. It's not the weirdest or grossest thing they've seen and it happens all the time, so they aren't bothered at all.