Not if he is not a natural born citizen and never qualified to sit in the Oval Office to begin with.
Fine...let's entertain this political fantasy.
A birther lawyer eventually finds a sympathetic judge and lawyers argue and voila...Obama is not eligible. You now have a judgement.
Do you honestly believe that the Legislative and Executive branches of the government will allow the Judicial branch to decide who will be president?
My guess is the Executive branch would dare them to try to enforce the judgement, while the two main parties in the Legislative branch would unite in telling the Judicial branch that it is exceeding it's authority.
And if you would follow the link I provided you will learn that much of this is NOT new territory.
According to that line of thought, neither was Chester Arthur the 21st president.