Duh!!!! For the last time, yes.
Let's divorce the concept of race from biology or some percentage of ethnicities or even the One Drop Rule. I had a wonderful class in undergrad that explained being black in America as a shared experience, history, and struggle. By that definition alone, yes, Barack is back. By this definition biracial does not exist. If you identify, classify, or are down with the struggle then you are African American.
I have read Dreams of My Father and from day one Barack experienced the duality of being both black and American. He has had people asking to touch his hair, wanting him to be the 'cool, black kid' they happen to know. He has been discriminated against but never let that hold him back.
IMO, people who want to reclassify him as biracial are people who have denied their position as African Americans and want a role model for their indecisiveness. Like, "hey let's all hang out here in the land of ambiguity." Because no one wants to feel the full weight of being African American, the contempt, stereotypes, racism, etcetera, etcetera.
But Barack killed that noise early on. The attacks he suffered during the campaign were not lessened by this "white half". No he carried the full brunt of it like so many of our people who are a grand mixture already.
If we reduce people to percentages then what do you have? Black people with new dumb labels across their forehead, the modern equivalent of the ubiquitous, "I have Indian in my family."
I will leave you a quote from W.E.B. Dubois:
"It is peculiar a sensation, this double-consciousness, this sense of always looking at one's self through the eyes of others, of measuring one's soul by the tape of a world that looks on in amused contempt and pity. One ever feels his two-ness, – An American, A Negro; two souls, two thoughts, to unreconciled strivings; two warring ideals in one dark body, whose dogged strength alone alone keeps it from being torn asunder."
The Souls of Black Folk
Not one percentage in there.