Yes they do have a pulse because even though they are dead, they still have a heart and it is still pumping so yea they would indeed have a pulse going.
If your asking about the first vampire that was created, then the very fist vampire was Mikael. He was the father of the originals, and the one that turned them.
While you are left at the end of an episode thinking that Jeremy will die from a self induced drug overdose and become a vampire, when the following episode picks up, we learn that Jeremy did not die...