Nope. Under the Twenty-Second Amendment, Obama cannot be "elected" President again. It does not say that he cannot be appointed VP and then become President again if the President is impeached or resigns.
OTOH, it is all academic. I don't see any chance that it will ever happen. Obama much prefers running things behind the curtain, so he can take as much money as he wants from countries around the world and doesn't have to pretend to show up for work.
Obamaramadingdong can’t serve as VP either. To serve as the VP, you have to be constitutionally eligible to serve as POTUS, which he is not per the 22nd amendment.
Also, he cannot assume the presidency via being Speaker of the House due to his being constitutionally ineligible to serve if both China Joe and Heels Up Harris were removed from office. The presidency would then fall to the next person in the line of presidential succession, the President Pro Tem of the Senate.