Maybe yes, maybe no. As Orrin Hatch wrote at the time:
The Constitution gives the Senate authority to determine its procedural rules. More than a century ago, however, the Supreme Court unanimously recognized the obvious maxim that those rules may not “ignore constitutional restraints.” The Constitution explicitly requires a supermajority vote for such things as trying impeachments or overriding a presidential veto; it does not do so for confirming nominations. Article II, Section 2, even mentions ratifying treaties and confirming nominees in the very same sentence, requiring a supermajority for the first but not for the second. Twisting Senate rules to create a confirmation supermajority undermines the Constitution. As Senator Joseph Lieberman once argued, it amounts to “an amendment of the Constitution by rule of the U.S. Senate.”
In fact, organizations like Judicial Watch were in the process of preparing briefs in the DC federal court before the Gang of 14 stepped in. It’s true that the courts normally frown on entering into this sort of legislative squabbling, but you never know!