If only she wasn't TOTALLY INSANE, of course. Got nothing to do with her gender. But rather, everything to do with the obvious fact that she was a couple of sandwiches short of a picnic.
Like I said before: Janice's obvious insanity means that nothing she says or does can ever be taken at face value
. Thus, it's easy to dismiss even the "Your world of starship captains doesn't admit women" line. (That is, if you don't believe that she was speaking personally about KIRK's world, of course.)
And like I also said: In the perfect future utopia that we all know Gene wanted to depict, it is inconceivable that he would leave just this one detail (women in command) out of it. If Gene was as sexist as a lot of people keep saying, Number One would never have existed! If a woman can be XO, then by definition, she can also be a captain. Simple logic.