I think the SCOTUS has already weighed in that this is not right/constitutional:

Constitution says Chief Justice presides when it's the president on trial.
Roberts already said he's not presiding because it's not the president being tried.

so, who is being tried? If not President Trump, then who? It can't be citizen Trump, that's not an impeachment.

This is in a weird area, but I think Roberts tipped his hand on the SC view.