Hey Bob,
I,m having fun, so bear with me while we play, "Pick apart the other guy!" A Code Forum favorite Game Show.... Kidding!
LOL
I can kick things around and disagree without getting upset.
Very unlikely a ground will open a 15 amp breaker from a 120 volt source unless there is already a good load on it.
The combined resistance resistance of the rod at the service and whatever electrodes are connected to the power company source would have to be less than 8 ohms. If you got down to 6 ohms it would take some time to trip, to get a 'fast' trip IMO you will need to get down to 2 or 3 ohms.
IMO you would need some unusual conditions to have less than 8 ohms total.
Bob