I would venture to assume that your citizenship status will matter only if you're applying to a state-funded program vs. private, very much like when you're applying to state-funded vs. private dental schools.
I even know of Canadians who've graduated from Canadian dental schools and successfully matched into residencies in the States, obviously after taking part 1 like the rest of U.S. applicants.
I personally think if you've graduated from a U.S. school, you'd sort of blend better with the rest of the applicants.