I reckon you'd be less likely to poo in labour if you have a non-induced birth. In early labour, most women get the runs, their body is clearing out for the impending birth. But if you are induced, you haven't started that process, so it would be interesting to see the difference... I know that happened to me, I had the runs, and no probs with anything else coming out in labour.
I was induced and was on the loo every 15-20 minutes while at the period pain stage. So no, I'm not sure if this is the case.