Trump Senate Trial

So, Im not here to argue about the merits of the trial of the second impeachment, but I see a interesting legal arguement that coud be forming with this second trial.

Currently the senate is going to have Senator, Leahy (D) preside over the trial since traditionally the pri temp presides over the trial of non presidents.

However the constution says different: when the President of the United States is tried, the Chief Justice shall preside.

So the question I pose is as follows: If Trump is being impeached for actions taken as president, should the senate trial be held as if he was a president?

My opinion is yes, if being tried for actions in office, he should be treated as in office for the entire process. (Obviously not remaining in office)