Napoleonrules
Banned
No one would be taking it to the Supreme Court or even think they could. Judicial review is not in the Constitution and was not established as a precedent until Jefferson's presidency when Madison wss sec of state (hence the name of the of the case Marbury v Madison). I believe that case would be in 1801 or 2I'm not sure if it quite works like that. If Adams asserts his authority, he's creating a precedent that the text of Article 1 Clause 4 is interpreted to imply a strong VP with actual responsibilities. That interpretation is entirely consistent with the text of Art 1 c4, and consistent with the other uses of the word "president" in the Constitution. Maybe the Senate doesn't like it, but they don't get to make the choice (unless John Adams, uber-schlemiel, lets them). The Constitutional Convention, the states, and the Electoral College all made the choice of what a Vice President was supposed to do and who the first one was supposed to be. Of course, if they disagree, they'll be free to take their case to the Supreme Court, but I think they'll lose badly. Or they can deal with it and try to get along with Adams.
And like I said, there's nothing except tradition preventing a later VP from assuming this type of role. I know LBJ wanted to. I pointed out Aaron Burr as a likely suspect because the political system was new enough that tradition wouldn't have been much of a factor in 1800.