But if Trump were convicted in this case, he and his lawyers would almost certainly argue that the trial was unconstitutional precisely because Roberts did not preside, directly in contradiction of the plain words of the text, rendering the judgement and the penalty of disqualification from office void. I, for one, am less interested in whether this is a compelling argument than I am in the fact that in what Democrats consider an ideal outcome it would almost certainly be made and would thus require an answer. The precise legal mechanism that would signal such a challenge — the refusal of the Federal Election Commission to file paperwork on behalf of his presidential campaign, a primary ballot access lawsuit — does not matter. Sooner or later, probably long before any actual voting, the courts would have to rule on the question of whether the Senate trial was conducted in a legitimate manner.
I cannot begin to guess how the Supreme Court would rule in such a case (with the exception of Roberts, who would obviously recuse himself). I also suspect that the justices would do almost anything to prevent themselves from having to rule one way or the other. If it had appeared possible even for a moment last month that Democrats were close to the 67 necessary votes to convict Trump, making future Supreme Court litigation on impeachment a near certainty, would Roberts have made the same decision? I doubt it.