I don't think it would have any effect on either vamps or virgins. Some quotes:
"White Court vampirism is a hereditary condition, passed along when interbreeding with humans, always breeding true."
"They might best be seen as a separate race, able to interbreed with humans (White Court vampires are born, not made—it’s hereditary)."
I see exorcism as intended to address cases in which a demonic being is squatting on the spiritual real estate of somebody else, so to speak. It would in theory work against a Denarian (though even the weakest Denarian would probably be able to resist any attempt at exorcism that didn't directly involve an archangel or better, which in turn wouldn't happen because it would circumvent the free will decision of the coinbearer). It wouldn't work against any of the vampire Courts, because their infection (in the case of Red and Black courts) or hereditary genetics (in the case of White) has actually changed/shaped who they are, rather than imposing a demonic copilot on them.
To support this, I would point out that if this worked, there would be no Fellowship of St. Giles, since all of those Red Court Infected would have been long since exorcised back to normal.