From the section you referenced:<p>&quot;He [the President] shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;&quot;<p>I think that your claim that the only role of the Senate is that it &quot;must be notified in the event the President has made a sole-executive agreement&quot; is a misrepresentation.  In fact, the Senate must vote to approve every potential treaty before it becomes valid.