Different zombie movies show different types of zombie – some fast, some slow, some a virus others a kind of madness. They all work in different ways, so I dont know how to judge how feasible they are!
I hope it can never happen though – genuinely, my biggest fear (just ahead of spiders) is a zombie apocalypse. I would not last long if it happened!
Like Lewis said, there seems to be different sorts of zombies in movies and books. My favourite book is ‘the Zombie Survival Guide’.
Historically, the first zombie reports appears to be from the carribean voodoo religion, and the word itself might be derived form ‘jumbie’ west indian for ghost or ‘nzumbi’ Kikongo word for spirit of a dead person. It turns out the puffer fish toxin Tetrodotoxin is used in some of the zombie powders of the carribean and this can cause paralysis and prevent response to stimuli. People poisoned with tetrodotoxin can appear dead and then make a miraculous recovery. Recent some synthetic cannabinoid drugs have caused people to have a vacant stare and slow mechanical movements, and a psychotic face eating episode in miami may have been at least partially induced by this.
While viruses and other infections can sometimes cause hallucinations and other weird brain effects, I have not seen any reports of the kinds of symptoms like observed for the toxin or drug overdose. Doesn’t mean it couldn’t happen.
So after all this, my answer is that it is possible, but not likely. But just in case, I read the guide anyway.