I think they might. We are not dealing with rules in regard to legislation, which is within the perview of the Senate and house, but this deals with the constitutional power and authority of the President to nominate Justices. The Senate has a constitutional authority to advise and consent. The Supreme Court has the authority to interpret that clause. Does it mean that a minority of senators can hold up the consent? Or does it require that the Senate vote these nominations up or down without undue delay?
I think that since this filibuster rule has not been used in over 200 years of judicial nominating procedures, that the SCOTUS very well may find that the Senate has engaged in an unconstitutional infringement upon the President's constitutional power to make nominations that will either be rejected or consented to following a reasonable investigation into their qualifications.
I am optimistic on this one. I do not believe that the Senate has the right to ignore a nomination, but I believe that the Senate has a constitutional obligation to give advise and consent upon each and every judicial nominee. Failure to act upon a nomination is an unconstitutional infringment upon the power and authority of the Executive Branch. This is not a political question. This is a pure constitutional question. The Supreme Court has an obligation to interpret the advise and consent clause if it is brought before it.