Sure, I suppose it's possible.
If you have ever read the "Maze Runner" series, there was this man-made disease that turned people into their insane and delusional selves; pushing them to the point where the virus in their brain just killed them. The infected also couldn't take care of themselves properly, so they were often infested with parasites and other nasty things and wounds, making them look similar to zombies. I think this scenario is entirely possible.
As for the actual Hollywood version (like rising from the dead, brain-eating zombies), I think it is unlikely, but still possible.