Yes, you can. Thought this suggests you are going to side with the Volkihar clan, as the Dawnguard would make you cure it at some point. Haven't played that side yet, so I don't know the full details there. Although Isran, the Dawnguard leader isn't going to say anything about the PC being a Vampire before being sent to Dimhollow.
But coming to Harkon while already a Vampire does give some unique lines/dialog, both from you and him, mostly the obvious comments. It is of course possible that you may become a Vampire because of those in Dimhollow Crypt, and by the time you reach the castle, you are already a Vampire.
Also a note - unlike the normal contraction, crossing to accept Harkon's offer is not like the usual infection. i.e you do not have to wait a certain amount of time, nor is it a disease you can simply cure. While curing it is possible, the potion/spell isn't going to do it. But once you accept, you'll be made a Vampire(or at least one of Harkon's blood if already a Vampire) within short order.