I might end up sounding like an acquaintance of mine, from WV, in saying this, but to Hell with it.
By the very definition of "undead", is depicted the 'vampire', AND zombies. But to be technical, in the meanings of each, the "undead vampire" is for one, a creation of some of the oldest myths known to man, which were grossly exaggerated by just about every story teller, writer, movie director known to the modern world.
Bram Stoker 'Immortalized' Vlad the Impaler, in his writings of "Dracula", anf thus, in a way, created the stereotype of the 'vampire' as many view it, today. Hence, the "undead". AKA, "Nosferatu".
Zombies, on the other hand, though my memory of the fictional works is foggy from the years, are the end result of a virus transmitted through the blood stream, which reanimates he dead cells, and thus brings the cadaver back to "life", but with an insatiable hunger for living flesh, and thus how and why they kill living people. But they can evidently still easily survive without it.
Real Vampyres, however, need to 'feed' to sustain their own health, if not their life. I don't remember much about zombies, at this point, though I know I've heard my fair share of interesting details about several different things (zombies included). Enough to make just about anyone wonder what really walks the earth.
In any case, based upon what I know, though limited as it may be, as I can't see any connection between the two, I would have to say that obviously, as a 'Vampyre' is still a 'Vampyre', the same principal goes for zombies -- a zombie is not a 'Vampyre'. Too many things set them apart? And hence, a zombie is made by a form of science, a Vampyre of Any kind is not. Though much of it is genetics, there is a much larger piece that makes the Real Vampyre what he or she is, which makes them completely different from any zombie.
That being said, I really don't think that either would have any effect upon the other.
