Correct. Of course, if Biden resigns, dies or becomes incapacitated, Obama can nominate anybody, or anybody who meets the eligibility requirements.
Of course, the nomination still has to make it thru a majority vote of both houses of Congress.
So ironic in many ways - I firmly believe that there is serious questions concerning Biden's mental capacity, and when the question of meeting eligibility requirements arises, of course there is doubt that 0bama meets them.