I wish that was true, but history shows that it isn't.
Biden’t signing of a treaty might look nice, but it isn’t binding unless it is ratified by 2/3rds of the Senate.
That was never true. Article II, Section 2, Clause 2 of the Constitution specifies "two thirds of the senators present," a provision that did not go over well with Patrick Henry at the Virginia Ratifying Convention. See the above link.
I didn’t think the president can alone sign America to any treaty?
ANY officer of Executive Branch of the government may sign a treaty, at which point the government has chosen to abide by and enforce them without ratification, as has been the case for forty years. See the link above. That's why Bush withdrew the signature for the treaty governing the International Criminal Court. See the above link.
So if 7 senators out of ten present in a hotel room vote for a treaty that ratifies it?