In effect, if he sits illegitimately, then nothing that he has done since his inauguration has any legal effect under the Constitution. Not only that, but since such would be illegal acts, he cannot legitimately compel the federal taxpayer to pay for them.
Thank you so much for your insights, dearest sister in Christ!
Apparently this is NOT true, because of a recognized legal principle called the "de facto officer doctrine".
According to the Supreme Court:
"The de facto officer doctrine confers validity upon acts performed by a person acting under the color of official title even though it is later discovered that the legality of that person's appointment or election to office is deficient."
- Ryder v. United States (94-431), 515 U.S. 177 (1995):