Not sure I agree with this statement:
At its Renton, Washington, plant, Boeing typically removes the pop-out, or non-functioning, door and uses the gap to load interiors. Then, the part is put back and the installation in completed.
Again, no first hand knowledge of how they do things in Renton on the 737 line, but in Everett, Emergency Exit doors are rarely used to load interior components for the simple reason that they are smaller than the main entry/exit doors. Since loading interior components is largely done manually, they want as much room as possible. While this is done both through the front and rear main doors, I've never heard of that being through an over-wing exit door.
Function E-E doors are often opened to provide ventilation, etc., both in the factory and out on the flight line (with safety straps applied across the opening to discourage people from falling out), but I seriously doubt that is ever done with a non-function exit 'plug'.