They will not refuse to hear this case. Mitch McConnell is filing as a plaintiff.
They do that quite often.
Just cause a Senator has an interest in the case, doesn't mean the SCOTUS has to take it.
I remember Senators had an interested in finding the so called line item veto unconstitutional and the SCOTUS, stating they had no standing with the court cause it didn't affect them.
So state had to make the challenge.
Remember lawyers and Judges do not think like normal people, they have been taught to make a straight line into a Mobius circle.