No. As part of the agreement to resurrect the rule on Motion to Vacate with just one person needed to call a vote, later measures were instituted and agreed to between the Speaker's office and the conference.

Part of those measures were allowing a confidential list to be drawn up by the SOTH in the case that a motion to vacate passed on the floor. The Speaker created a secret short list of names to act as his temporary replacement - in the interest of continuing the business of the 118th Congress with as little interruption as possible.

The Speaker pro tempore (Patrick McHenry of NC) has all the powers of any elected Speaker of the House, HOWEVER the critical mission as pro tempore is to simply oversee the continued functioning of the House according to the calendar already in place. Any unusual or radical actions taken by a pro tempore Speaker would be unacceptable and I believe that process exists to negate such measures taken while holding the office in pro tempore.

When a new speaker is elected they will vacate the chair for that person. They basically only are there to just make sure the House keeps moving along during session.