The Vampire craze has been going since Bela Lugosi donned the cape back in the thirties. Not a decade has gone by where Vampires weren't in movies, books, comics. Of course the twilight saga has brought ushered in another generation, mostly females, but there's nothing new about people being crazed for vampires.
Actually I like this topic. I think you're right about Kirk. He'd easily get Chekov, Sulu, Uhura, Yeoman Rand, but I do think by that point Spock would stake him or expose him to the right kind of light.
Actually I think Picard would get his entire crew. He'd start with Troi, then work his way through. Data would be the greatest challenge, but since they all trust him implicitly he'd easily fool them.
Sisko I don't know about that. I watched DS9 but I can't think of whether he'd succeed or not.
Anyways, don't let them get ya down. Not a bad idea for a thread in my opinion.