Well, your classic "Living Dead" zombie was rather slow and ponderous, however more recent research as shown in documentaries such as "Resident Evil" and "28 days/weeks later" and "World War Z" suggests they can indeed run, to a lesser extent "Walking Dead" too, although I guess it depends on your definition of zombie. However, what we must always keep in mind is that they are utterly relentless!!
BTW, I like the idea, it looks like a bit of fun.............and when it all hits the fan I wonder who'll be laughing then?