Okay so I guess I'll try to defend Booker, even though I'm on team Alucard. This fight doesn't have to be restrained to just being a deathmatch where Alucard would obviously win; but if we were to go along these lines there really isn't anything to say that Bookers possession ability wouldn't work on Alucard, since we do know that Alucard can be controlled by a magical force based entirely on his own series.
And then? Does Alucard kill himself upon the end of possession? Does Booker try to kill possessed Alucard until that ends? Booker, and for that matter everyone at street level, gets murdered by Alucard. He wins this fight, there's no point arguing against it.
Sorry if I sound pissy, I'm not trying to. I think in our back and forth, we're both right on points, and we're both wrong on points.