This whole thing is silly. No court is going to rule that where a document says "he", it does not mean "he, or she", unless that document has some particular purpose to refer only to men. The Founders wrote the Constitution with exclusive use of the masculine pronoun because it never occurred to them that a woman would seek the office of the presidency. (History is almost totally devoid before 1787 of female politicians who were not royalty.) Documents are still written today with only the one pronoun, because writing both is cumbersome and repetitive.
Bottom line: the Constitution does not say "the President shall be male". Therefore there is no bar.