Not really. Yes the President has final say, nothing in the USC says anything about prohibiting the President from using the VP as a "superadvisor". As a matter of fact, I would argue that is a good role for the VP.
Right -- there is nothing in the Constitution limiting how much advice/guidance the President takes from the VP. Purely official acts, such as the signing of legislation, appointments, etc., must be done under the signature of the President. But there's no problem with the President letting the VP run meetings, make decisions that are ratified by the President, etc.. Sort of like a Chief of Staff on steroids. I don't think it's a bad model, actually, if done correctly.
The best example of this might be in the military, with the distinction between the Commanding Officer, and the Executive Officer. The Exec runs the unit on a day to day basis, but the CO is the one who sets the tone, overall agenda, etc..