well, do the bodies of zombies still work? does the stomach and digestive system still works? it is a dead body, I don't really know what works and what doesn't.
so no. Zombie's bodies don't function like living humans. They don't live off eating the flesh of the living, they just have a desire to bite things that are alive. Whatever enters their stomach doesn't get digested, it just sits there.
From the The Zombie Survival Guide: Complete Protection from the Living Dead:
"Recent evidence has once and for all discounted the theory that human flesh is the fuel for the undead. A zombie's digestive tract is completely dormant. The complex system that processes food, extracts nutrition, and excretes waste does not factor into a zombie's physiology.
Autopsies conducted on neutralized undead have shown that their 'food' lies in its original, undigested state at all sections of the tract. This partially chewed, slowly rotting matter will continue to accumulate, as the zombie devours more victims, until it is forced through the butt, or literally bursts through the stomach or intestinal lining.
While this more dramatic example of non-digestion is rare, hundreds of eyewitness reports have confirmed undead to have distended bellies. One captured and dissected specimen was found to contain 211 pounds of flesh within its system! Even rarer accounts have confirmed that zombies continue to feed long after their digestive tracts have exploded from within."
Zombies Don't Poop!