Didn't they start the sexy vampire trend in the 1931 Dracula (and the Broadway show that preceded it), where Bela Lugosi played him as a suave, charming Eastern European aristocrat?
To the same extent as most suave, debonair men were sexualised on film in those days, yes. Which was to say not much. The sexuality and seduction aspects of vampirism were downplayed and limited to implied scenes - a lot of films preferring to imply that a vampire's control over its victim was hypnotic, rather than seductive.
It wasn't until the late 50's and early 60's, with the introduction of more liberal views on censorship in some European countries, that cinematic vampires started to become more heavily sexualised.