Hello, Don. If the rod isn't effectively bonded to the rest of the Grounding Electrode System, the rod will serve to ensure a high voltage gradient exists during a lightning strike on the system with the pump system (pump, phase conductors, OCPD) taking the full brunt of it.
The pipe and rod, if meeting the descriptions of 250.52, would be connected to the grounding electrode conductor, not the grounded conductor.
On a 480V grounded-wye system, the ground rod at 25 ohms draws 11A. The grubs and earthworms hate it, but it's not the fault path you want the current to follow back to the service. For the pump motor itself you'd have an equipment grounding conductor running in parallel with the phase conductors all the way back to the panel, sized sufficiently (as are the phase conductors) so that a ground fault at the pump would pass enough current through the EGC to clear the OCPD quickly.
As ptonsparky and jwelectric said, you'd also have to run a bonding jumper back to the grounding electrode system if the pipe and rod conform to 250.52. I'm not positive on this, but I don't think it's kosher to make the EGC pull double-duty as a bonding jumper to the GEC, so you'd need separate bonding.
If I typed any slower I'd be pushing daisies.
Is the fourth wire acting as the neutral on a wye-connected motor, or the equipment grounding conductor?
Regards,
Dan