Legal Question in Constitutional Law in Texas

Not successfully. That would be true even if McConnell had a clear duty to allow a vote. There's no authoritative law either way, but he's probably right that the senate can refuse to cooperate. Whether to do so would then be a question of politics rather than law, which is just one of many reasons why the courts would not intervene. Another is that courts have to respect the constitutional separation of powers. They can't tell senators how to vote on particular bills or nominees, just as the senate can't tell judges how to rule in particular cases.