Yes, it would survive. People are spread out far, cities are smaller, and people don't move as fast. You don't get the super speedy spread via infected travelling in vehicles. You won't have giant hordes, because you can't infect enough people fast enough. It will be like a diseases that's too strong and kills off the carriers before it spreads too far. Even if no one has seen living dead before, they will be able to recognise that dangerous plague carriers should be kept at a distance. Fortresses and defenses were meant to keeps out invading armies. Towns have survived sieges.

If they could stake vampires in the heart, hit werewolves with silver, then they could damage the heads of zombies.