Technically, a subject pronoun such as he should not serve to stand in for a possessive such as Obama's.
The reason:
A possessive serves not as a noun but as a MODIFIER, and the referent for a subject pronoun must be a NOUN.
That said, virtually every reader of the sentence above would understand that the intended referent for he is Obama.
Further, pronoun ambiguity is a low-priority error on the GMAT.
A good rule of thumb:
If an answer choice includes a potentially ambiguous pronoun, do not immediately eliminate the answer choice.
Instead, look for an answer choice that avoids the potential ambiguity and is free of errors.
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