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 had similar thoughts when I was preparing for DDs birth but when I was very unexpectedly admitted to hospital with PE and inductions were being bantied about I got very worried about pooing during labour because I wouldn't get the runs etc that you normally do in natural labour.

I went into hossie on Friday afternoon - on Saturday morning I made sure I emptied my bowels in case I was induced that day but I wasn't induced. On Sunday morning I made sure I emptied my bowels but I couldn't (slight constipation) and then they told me that that was the day I would be induced due to my liver function and I pannicked

During labour I kept asking to go to the toilet... I never did get that poo out on the toilet or in the throws of labour but I did reach a point where I would not have cared if I did.

The next day though I was a pooping machine LOL