If your carotid artery were punctured with something like, oh, say, a vampire tooth, wouldn't you die?

Since you obviously like to read non-fiction and fiction books. Pull out your encyclopedia (Google) and look up how a leach operates. It will get on you, draw blood from you until they are completely stuffed and fall off leaving no leaking hole in their absence. Because of the secretions they have, you dont even know you were bit. Maybe that is why vampires were called Blood sucking leaches in the "Lost Boys". So in a fictional world it is very possible to survive a bite. Wear that garlic necklace with pride or join the world of the undead.