NEWS: SCOTUS will not immediately hear the case over Trump’s immunity claim in connection with the Jan. 6-related federal charges he faces in DC. The DC Circuit, however, has already expedited the appeal to be heard there in early January.
No. If the appeals says no immunity. Things go as normal even if Trump files an appeal. Remember no one has a right to a Supreme Court hearing. So if they deny cert for the appeal no time is lost.