They did when we impeached Clinton, and recounts in Florida. They have been involved in other Constitutional crisis'. If Republicans try the nuclear option the rats will claim it is illegal, and send lawyers to the SCOTUS. Bank on it.
IMO the SCOTUS would side with the rats based upon a long history of previous Senates abiding by the rules of the last Senate.
We might reasonably disagree on other issues, but I can say without any doubt you're wrong here. If the libs appeal to them, the Supreme Court will stay the heck out of it. They will say that the Senate makes its own rules.
That's what they do in this kind of situation every time.