Not necessarily; he faces him but he just wasn't alone. In fact this is the first Castlevania game to have a Belmont tag-team match vs. Dracula!
Also, I don't believe Dracula was even killed at any point in this game. He just teleports away, and Alucard even says that's not how "a vampire is supposed to die," or something like that. Someone might say "but the castle crumbles at the end, thus signifying Dracula's death," but that's not the first time such a thing has happened. If you recall CVAdventure's ending, Dracula is "killed" and the castle crumbles, but Dracula in bat form is seen flying away. In fact Alucard's MoF ending can be seen as an homage to CVA's ending, now that I think about it.