No. Congress has its own recourse, which is impeachment.
Section 4 of the 25th Amendment would cover situations such as when Woodrow Wilson had had his stroke, and couldn't fulfill the duties of the office. A similar situation might occur if Trump does something like .... went actually nuts, or stopped showing up for work.
Or for any reason at all, really. 'Inability to work with Congress' or 'Inability to distinguish between reality and fantasy' both work. Nothing in the section requires a physical or mental illness, just that a majority of head of the executive departments... or any other body determined by Congress, think he is incapable of performing his duties.
I'd wager Congress has included itself as one of their 'other bodies'.
----
Text of the 25th Amendment, Section 4:
Section 4. Whenever the Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide, transmit to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall immediately assume the powers and duties of the office as Acting President.
Thereafter, when the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that no inability exists, he shall resume the powers and duties of his office unless the Vice President and a majority of either the principal officers of the executive department or of such other body as Congress may by law provide, transmit within four days to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office. Thereupon Congress shall decide the issue, assembling within forty-eight hours for that purpose if not in session. If the Congress, within twenty-one days after receipt of the latter written declaration, or, if Congress is not in session, within twenty-one days after Congress is required to assemble, determines by two-thirds vote of both Houses that the President is unable to discharge the powers and duties of his office, the Vice President shall continue to discharge the same as Acting President; otherwise, the President shall resume the powers and duties of his office.
