Article II, Section 1
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
If the Supreme Court finds him not eligible, not only need he not be impeached, he cannot be impeached. He'd have never *been* legally President. Only someone eligible to the office can lawfully be President. Impeachment and conviction in the Senate is for removing a *President*, or other official, not an ineligible usurper occupying the Oval Office.