The treaty must also pass scrutiny under our Constitution, and thus, even if the Senate did ratify by a 2/3rd's vote, the SCOTUS could still strike it down.
What planet are you living on? When was the last time this administration bothered with the former Constitution?
In fact, what is the current score, over the past 30 years, for the SCOTUS bothering with the former Constitution?
Start with CO2 and work backwards on the decisions. There has been no SCOTUS (or their underlings in the Circuit courts) supporting the former Constitution for many years. So your "hope" is really a "pipe-dream"....