No. There is something called the de-facto officer doctrine which says that any acts performed while someone holds office are valid even if it is later found that they are ineligible to hold that office. If Obama is found ineligible and removed tomorrow that would not change anything done to date.
“de-facto officer doctrine”
Thank you. I never knew this, but it surely makes sense. Sadly, however, it also provides an incentive for illegal office-holders to cling to their offices as long as possible, knowing that every act they conduct in the interim will have the same force of law as if they’d secured that office legally.
one whose acts, though not those of a lawful officer, the law, upon principles of policy and justice, will hold valid so far as they involve the interests of the public and third persons, where the duties of the office were exercised . . . . under color of a known election or appointment [that would otherwise be] void by reason of some defect or irregularity in its exercise, such ineligibility, want of power, or defect being unknown to the public
How many lawsuits have been filed on behalf of the public claiming Obama ineligible? It was known and protested by the public prior to his election and continues to this day.