It depends on whether she was married or not.
If married - no citizenship.
If not married -citizenship.
Unless you find case law or a loophole that protects poor bastard baby from lying commie bigamist father.
Not quite.
True, it does suffice if you are a bastard born of an American citizen overseas.
But if you are an American married to a foreign national and living in Foreignnationalisatan, your kid is a Foreignnationalisatani by birth.
Also if you get knocked up by an American (military or civilian) in Foreignnationalisatan, and you are Foreignnationalisatani, your kid is also a Foreignnationalisatani.
By itself, one American parent is no guarantee of American citizenship.
Nor is Citizenship, by itself, a qualifier for holding the office of President.
No. If she was married, she has to have met a residency in the US requirement, in 1961, that was 5 years after her 14th birthday. She was not yet 19 and so she didn't meet that requirement. If she was not legally married (where the birth took place) then she only needed to have resided in the US for one year. But all that is about being a citizen at birth, and is provided by statute. A statue cannot change the meaning of a Constitutional term, and so he would not be a natural born citizen, which is the Constitutional requirement.
If born in the US, with his mother married or not, and his legal father not a US citizen, he is likely also not natural born. I say likely, because it's never really been adjudicated. Only one other President hid his records, Chester Arthur, whose father, it has recently been discovered, was not a US citizen at the time of Chester's birth, although Unlike BHO Sr, he did eventually become one, when CA was 14.
Arthur was born in Vermont, never lived outside the US, and had the same father from the time he was born until his father passed away. Quite a Contrast to the Current resident of the Oval Office.