Well let me ask this. What happens if they DON'T get the votes they need? Does it just sit around until at some point down the road they have a big enough majority of gun haters in the Senate, and then the Senate just trots it out and approves it in the middle of the night? Not having the votes NOW doesn't mean they won't have them at some point in the future.
IIRC, yes. Once POTUS has signed said Treaty, the Senate can Ratify at any point in time (regardless of failed Ratification votes), unless and until POTUS has Abrogated said Treaty. (POTUS being an Office, not a Person)
IMO, it seems a bit open-ended. Also, IMO, "aid and comfort" should be a consideration.