You don’t need a vote to find out who supports something and who doesn’t.
It can't be debated because it will never reach the floor. It's not going to be marked up in committee debating which clauses Biden has violated. There will be no hearings or mention of any kind anywhere.
George W. had impeachment proceedings filed against him dozens of times, but it was also meaningless because the House was controlled by the Republicans. It was just filed away and forgotten
The House doesn't even have to do anything. It gets filed and then - nothing. It will be completely ignored. They could file impeachment proceedings every hour, but since Democrats control the House, it will be ignored.
Greene filed her impeachment proceedings in the House in January during Biden's first week in office. Again, when the Republicans take the House in January 2023, then any impeachment filings will have substance - until then, this is just show.