Really, probably not.
You can drain roughly 1 vitae a turn or so. You can drain another 1 through a certain discipline. Also, the loss of this lifeforce would cause injury to servants as they are spiritual beings. So the more the vampire feeds, the harder and harder it gets to slow her down. And once again, there's Protean, specifically a certain power that allows your hands to grow GECKO PADS to assist you in holding and grappling prey. So keeping hold of a Servant theoretically won't be a problem.
Our theoretical vampire with Bloodworking as a discipline as well can then cause an enormous amount of damage within the grapple using his powers, combined with damage during the grapple through the protean power, and then the damage from the fangs.
Then add in Vigor for MORE damage, and then you get Rider both being drained and damaged faster than repair is possible.