And also, I should say that this might involve not only International law, but also U.S. Federal law (when pertaining to the U.S. specifically).
On 20 January 2009 we ceased to be a nation under Rule of Law. The majority in Congress acts boldly in criminal insanity. An illegitimate usurper holds the Presidency.
Still, the question is interesting: if Obama is held a natural born citizen dint of mother’s citizenship, yet he is also a citizen of another nation — Kenya, Canada, Indonesia, or whatever — can he enter into treaties?
My first impression, based on laws of agency, is yes. Perhaps you can summarize JB’s argument otherwise.