When they get there is irrelevant. The rules are the same. Not sure why people think stopping the investigation now is going to somehow...stop it. Indictments have been handed out...documents have been sealed...deals have been cut...we are just now hearing about stuff that happened months ago...at this point I would say the investigation is actually pretty much over.
It's got to go to the Supreme Court first...and since it is an actual written document that shows that it already happened in the Nixon case, more likely than not precedent is going to win.
Here is a question...say they decide to impeach trump...how would that even get to the supreme court?
Here is a question...say they decided to indict and just flat out arrest Trump without impeaching him, how would that get to the supreme court?