This case already happened, specifically in reference to immigration, 70 years ago: see Knauff v. Shaughnessy[0] (1950).
> The exclusion of aliens is a fundamental act of sovereignty. The right to do so stems not alone from legislative power, but is inherent in the executive power to control the foreign affairs of the nation. When Congress prescribes a procedure concerning the admissibility of aliens, it is not dealing alone with a legislative power. It is implementing an inherent executive power.