However, if there is a problem with the gas pedal start being triggered by a faulty overdrive relay then you can get a grinding noise because the starter motor is smashing on the flywheel ring gear.
The OD and it's relay is a totally separate system to the starting circuit but you may be thinking of the regulator. On some of the cars there was a circuit which provided a starter safety interlock by running the starter relay ground side thru generator so starter couldn't engage once generator was putting out a voltage equal to battery. The circuit worked essentially the same as an idiot light circuit. Believe that was only on the senior cars and not on all of those at that or on the sixes. There was a bulletin to remove that particular circuit and provide a direct ground if needed because of issues of not being able to engage starter at times.
You do bring up an excellent point about the carburetor switch though. If that is out of adjustment or for some reason the vacuum cannot hold the interlock ball in it's engine running or safety park position, it could be engaging the starter prematurely. I don't believe the sixes had the large Autolite gear reduction starter but the start relay inside the solenoid housing on those can also act up.
