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.
How can someone not eligible to an office hold it, other than de facto? It's a logical impossibility.
Yes he is the de facto President, but that would cease to be the case once it was adjudicted that he was indeed not eligible. No one would be bound to obey his orders, nor would he legitimately be able to sign bills into law, nor do anything else that the President may do.
How what he has already done would be handled is another matter, and even I'm not so arrogant to believe I have any clue how that would all happen. But it certainly would be fodder for whole generations of lawyers.
That is not what is in dispute, at least here. The situation simply is ... and that defies logic and causes us all to go into various states of Cognitive Dissonance.
Yes he is the de facto President, but that would cease to be the case once it was adjudicted (ajudicated) that he was indeed not eligible.
The opinion of either the Federal District Court in DC, and the Appeal to SCOTUS, upholding that he was ineligible, would certainly be noticed in Congress. But then Congress would still have to get it together to Impeach, and Convict. Faker, Fraud, or Fool though he may certainly well be, only congress can remove him. Ironically, the Constitution he violated, actually now offers him a great deal of protection.
I believe your real question is, "If The SCOTUS were to uphold an opinion that he was ineligible, wouldn't Congress immediately Impeach the SOB in the House and immediately Convict the commie punk in the Senate?"
Answer: "Depends on who's in Congress, and what your definition of immediate is." And no matter who's in charge, I am willing to bet that you wouldn't like their idea of "operating in a speedy and efficacious manner."
At any rate, there is absolutely nothing about his eventual removal from office that would be automatic upon the findings of any court that he was ineligible.