If the marriage was in Kenya, it may very well have been official, since polygamy is legal there, and AFAIK, was legal in 1961 when it was a British Colony, but under a fair amount of local rule. I don't think it was in Kenya, nor do I know if it occurred at all, but since Stanley Ann's whereabouts from late December of '60 until late August of '61, are pretty much "unknown", it's possible.
However if BHO was born a bastard, and outside the US, then he was a citizen at birth under the law that existed at the time. Not natural born, but a citizen. But if SA and BHO Sr were married and the birth was outside the US, he wasn't a citizen at birth, and unless later naturalized, is an illegal alien, occuppying the White House.