Allow me to bring you up to high school level civics:
He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;
It's 2/3 of Senators PRESENT, not two thirds of the Senate. There have been treaties ratified in this country without a committee vote, without a quorum, and without a recorded vote. As for treaties becoming effectively enforceable upon signature, read the link about the Vienna Convention on the Law of Treaties. You're clueless.
I am full aware of the 2/3 PRESENT stipulation. I think that it was written that way to force senators to show up for such important votes and actually cast a vote. First of all, the Senate must have a quorum in order to hold any vote, i.e. 51 senators must be present to conduct business. Second, if the Rats tried to hold a dark of night secret vote to pass this, or tried some shenanigan like that, they would be crucified and they know it. You can bet your bottom dollar that there would be a lawsuit to overturn it before the ink was dry on the first editorial.