Yes he would be removed. But why? Because he failed to qualify.
If you write and sign a check, don’t mean it ain’t gonna bounce. The electors did not even consider if he was qualified. The rank marxists chosen to elect Obama would not have performed their duty.
No, because he would be found to be Constitutionally ineligible. It's after the fact. The election was held and the Electoral College has met and Obama is president. If he is removed from office for any reason - death, health, impeachement, or even ineligibility - then Biden will be president.