Yes
He has immunity
BUT... even if the executive is under legal theory constitutionally unitary, it isn’t actually unitary, it consists of individual people who act based on their own perception of legitimacy, and when the President abandons the principle of government of law and not arbitrary individual will in dealing with the courts, well, that also threatens the theoretical infrastructure that binds the people carrying guns in various executive departments to his authority, and we can very quickly end up in one of those highly unpredictable periods of history that produces lots of really neat stories to read about afterwards but is somewhat less pleasant to live through.