I suppose it would depend on the lore? If they have basic bodily functions they could poop. But then I don't think that would be considered "dead." The Walking Dead series, I think, showed very limited and primal brain activity at:::::::SPOILERS:::::::The end of Season 1 (rage and hunger). The digestive system is kinda nuts, so my vote would be no. No peristalsis = no poop.
Also, I made an account just to post this. Gratz on the attention grabbing headline!