It may well have a lot to do with his citizenship if for example it can be proved that he was not born in Hawaii....
He could only be a naturalized citizen at best since the law applies differently to Illegitimate children.
Also according to The Hawaiian Health department Vital records website the state of Hawaii will issue an amended birth certificate if the person was born outside of the United States.
Frankly I don’t know what that means but it sounds like they will issue one either way.....
But whether or not his parents were married is irrelevant, because the law in 1961 was that BOTH parents had to be US nationals (at least) to confer birthright citizenship.
If he was born outside of the US (which I think is very, very unlikely), then he's not eligible to be President. If he was born in Hawaii (or another state), he is.
In either case, since BHO Sr. was never a US national (and could not have been legally married to S. Ann Dunham under any circumstances), his parents' marital status is irrelevant.