Even if Trump had never verbally disagreed with the Chief Justice, Roberts would not be an impartial judge. Whatever dirt the Democrats have on him which caused him to switch his vote and save Obamacare would probably motivate him to side with the Democrats as much as he can while still pretending to be impartial.
But there is almost no role for the CJ in the hearings. He “presides” over them. I don’t think - or know of - any specific powers he would have except to appoint administrative assistants. It’s not like a regular court where he can rule on evidence or process. In the trial of POTUS Johnson, the CJ presiding over the case did make some unilateral procedural rulings but his rulings were overturned by the Senate.