Don't see what real benefit you would get from it. Unless you completely cleaned and sealed the heater core, you may risk damaging the core from the junk left in there. In addition, you are removing some amount of coolant from the system and that might change the coolant temps. Corvettes with the C68 Climate Control System uses the heater as necessary to maintain cabin temperatures. In addition, you may need heat for defogging the windshield or dehumidifying the interior air.
An old trick for helping with coolant temps and overheating was to turn the heater on full hot and the fan on High as the heater core works just like a tiny radiator.
Moving the temp control lever to the "Cool" position should shut the airflow door from the airbox. If the 84 has a coolant flow control valve, it should be actuated by moving the operating lever away from "Heat". The door and the valve operate by vacuum, so if youare still getting heat, I would check the operation of these two items. Not sure about the 84's but does the fan run on low speed all the time? If so, install a cutoff switch to the wire going to the fan motor to stop the fan.