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A great post on the legality of all things filibuster. Scroll down and read.
Money quote (emphasis mine):

Therefore, just as the Senate may delegate the impeachment power to a
committee under the Senate rules that may never send the matter to the full
Senate, so can the Senate do so in using its appointment powers. The notion that the Senate must vote on every nomination and cannot use it's internal rules to obstruct or prevent that occurance is without any historical support and against the greater weight of Senate precedent and constitutional interpretation by the United States Supreme Court.

This is a really good site with legal references. Good luck on that bar exam!