I'm not to sure whether it is a fix, as all the relay will do is act as a another switch where the wire from the ignition barrel is now switching the relay and not the solenoid of the starter motor; but yes less current will run through the wire off the ignition barrel. (I maybe wrong
) When i first had my HPE with plenty of electrical problems that was one of the things i got rid of, as my personal opinion was that it is another thing that can go wrong, the cars never had such item fitted from new and if somethings wrong then the item whether it is ignition barrel or starter motor will be replaced, and not things done which in the end may still not solve the problem.
As you've said, if you fit an ignition barrel you know is fully working and the problems solved, that would be it, if not could be the starter. On my delta i had it where it would click and click and click then would engage to start the car, and that was purely the starter; i regualarly used the car and have done for the last 30k miles in 2 years and it starts everytime first time