First, an archaeologist wouldn’t carbon date something. It’s not his job. This kind of analysis belongs to the archaeometrist, thank you very much!
Next, using carbon dating on a vampire raise really interesting questions. Because, you see, you can only carbon date completely dead things. Basically, the body absorb Carbon 14 while it’s alive, and after death, this radioactive element slowly decompose (half of it every 5730 years). When you measure how much is left, you can know how long ago the person/plant/whatever died. Going back to the vampire. Officially, vampires are dead. But they feed on human blood, living humans. I’m not sure of the logistic of carbon 14 linking itself to a body, but I think it would false the result. The good news is, as vampire can talk, they would be able to confirm or not. Meaning that we would be able to create a template and see if drinking blood reset your quantity of carbon 14, or if you can still get the age of death of the vampire by removing whatever carbon 14 they ingest through blood. But I think it would depend of how much blood they had ingested since their passing, and a lot of other variables.
The other question is: how dead is a vampire? Do they still breathe? How do they interact with their environment? Would that be enough to keep their carbon 14 at “normal” level? If so, they would be considered alive by this dating technique. Wouldn’t that be an emotional journey for our poor vampire?