Ann married a British transient. Upon marriage did she get British Citizenship? Ann Marrying Obama Sr. I believe gave her HIS status, and citizenship follows the father in any case. Obama was Born British and may have a 14th Amendment claim to citizenship. Anyone making a 14th Amendment claim for citizenship by definition is NOT a Natural Born Citizen because if they WERE an NBC, they would not NEED the 14th Amendment.
Ann’s status changes when she got married. That much is certain.
I guess it depends on which train of thought you wish to follow regarding the interpretation of the 14th amendment. Either way, He could receive citizenship from the 14th under one interpretation of it, and he could receive descent citizenship from his mother from the Acts of Congress of 1922 and 1934. (A Citizen by statute is NOT a natural born citizen.)
No Ann did not get UK citizenship by marriage even if the marriage was not bigamous. Nor would she lose her US citizenship automatically in a non-bigamous marriage because that was changed by law in the 1920’s, IIRC. Previously, a woman automatically did lose her US citizenship when she married an alien.