The presence of the two-thirds requirement for advice and consent on treaties pretty much indicates a requirement that Senate have actively established its consent. That said, the procedure for doing so is up to the Senate to decide by rule and need not even be by a majority
Interesting that it uses 'present' rather than 'in existence'. Has anyone ever tried to ram a treaty through by only letting a certain number of Senators have knowledge of a given ratification session, leaving the rest unaware of what is going on, as a political manuever? - with this scenario, a treaty could be approved with barely any votes.
A similar technique could be tried here.
I believe the rules of the Senate would prevent this from occurring, but the Constitution might not necessarily prevent this from happening if the rules of the Senate were changed.
On the topic at hand, it could work.
