In a state that does not allow civil unions or marriage between two same-sex people, can a transgendered person marry someone with the same genitalia?

I know that legally, two people of the same sex cannot get married or get a civil union in many states. Does this law extend to two people who have different genders, but the same genitalia? I have been thinking about this because I know a man who is male who dated a woman who is male as well. The woman has a penis but is very much of the feminine gender. They are no longer dating but if they were, could they legally get married? If whoever married them did not know that she had a penis and therefore thought she was female would the marriage be null and void if it came out that she had a penis? Does anything change if the person is a pre-op transexual and has surgery scheduled?