I don’t think they even have to take it up. House violated the Constitution half dozen times according to Dershowitz. Damned thing’s null and void on its face.
You may be correct from a Constitutionalist point of view.
However who knows with Schumer running the Senate?
Pelosi didn’t even run the first impeachment through the Judiciary Committee (Nadler), instead she used House (un)Intelligence Committee (Schiff) as her “point man.”
These Democrats don’t give a shit about the Constitution or historical precedent.