So Stalin, or Dolphie, or OBL could just knockup some merkin skanks, take em home and raise em to be good little fascists, and the son of Hitler would be eligible just because he WASN'T married?
Parentage has everything to do with citizenship, not marriage.
Blood relationship is a key component of U.S. citizenship law.
At birth such a child would have the unitary US citizenship of the mother because it would have no legal father for citizenship purposes (different from legal child support purposes introduced into the law in recent decades).
Whether such a child would be NBC has not been declared by SCOTUS under Minor v. Happersett, IMO. But not being subject to, for example, being drafted to fight in a war against the US if the child visited the country of his biological father would negate the long-standing concern regarding dual citizens, which bastard children are not.
There are residency requirements for being POTUS so a child of UBL would have to return to the US for the specified number of years and reach the specified age. At least the mother would have to be a US citizen, unlike anchor baby Anwar al-Awlaki.