No. The Supreme Court ruled that a sitting and former president, "enjoys no immunity for his unofficial acts, and not everything the President does is official. The President is not above the law. But under our system of separated powers, the President may not be prosecuted for exercising his core constitutional powers, and he is entitled to at least presumptive immunity from prosecution for his official acts. That immunity applies equally to all occupants of the Oval Office".

If an action is not within the President's core powers, then it's dependent upon the courts to determine if the action fell within an official act or not. If it's not, then there is no immunity. If it is, then the Government must show that applying a criminal prohibition to that act would pose no “dangers of intrusion on the authority and functions of the Executive Branch”.

In other words if a President's actions are:
• Within their exclusive constitutional powers - absolute immunity ('exclusive' meaning the power is not shared with Congress, such as granting reprieves and pardons)
• Official act outside of those core Constitutional authorities - Presumed to be immune unless shown otherwise (immunity extends to the “outer perimeter” of the President’s official responsibilities, covering actions so long as they are “not manifestly or palpably beyond [his] authority")
• Unofficial act - no immunity
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* Syllabus, Trump v. United States, No. 23-939 -https://www.supremecourt.gov/opinions/23pdf/23-939_e2pg.pdf
* Powers of the President under the Constitution - https://constitution.congress.gov/browse/essay/artII-1/ALDE_00000243/