Before the Electors vote - The Electors would vote for any person who is Constitutionally eligible to be President. It is not necessary for such a person to have been a Presidential or VP candidate.
After the Electors vote - Assuming the Obama Electors vote as expected, Vice President-elect Biden would become Vice President and Acting President at noon on January 20 pursuant to Section 3 of the 20th Amendment. Obama would trapped as President-elect, never to become President.
I love your scenario!
And the title of President-Elect fits his morphed crapping eagle that hijacked ‘presidential seal’ and his current title on his transportable podium.
Barry could still traipse across the globe as an ambassador of wanna-be POTUS and the Left would be delighted to further delusion!