[J. Tithonus Pednaud]

Interesting, my initial thought is that it would depend on the kind of Zombie. If you are talking Romero zombies, it seems initially unlikely as the circulatory system has ceased (open wounds seep but do not bleed). It's logical then to assume that the gastrointestinal system has shut down as well.

However, both Romero and NOTLD zombies do have limited muscular control, so I suppose - as it is possible for zombies to actually swallow food (using muscles) - and chemical digestion technically continues for a time after death, it is also quite possible that the rest of the digestive and elimination process would still function for a time.

Regardless, it's also important to note that the human body does generally release its bowels following death, this I can certainly attest to from my days as an embalmer. So, a new zombie may 'poop' but not really in the traditional sense. Rather the excrement in the bowels at the time of death would seep out due to gravity and muscle relaxation.

Given that last point, I suppose its safe to say that 'fresh' zombies do 'poop' though said' pooping' is not conventional and the process would not be a regular biological function.

The 'real' zombies of Haiti of course 'poop'.

Marvel Zombies do not seem like real zombies in that they are sentient and alien in origin. Their strange lip -devoid grimace looks more like a mutation than a simple reanimation.

I mean, do they actually die before zombification?

I'd wager that they do indeed poop like any living organism. They appear to digest whatever they eat. They often appear with distended bellies only to appear later slim and hungry again. That denotes some sort of metabolism or digestion.