Grounding electrode conductors must go from the electrode (water pipe in your case) to the service equipment. Read the definition of service equipment and you will find that it is basically a breaker or set of breakers (not more than 6) that are used to shut down the building. Everything after that is "other than service equipment", and no the grounding electrode conductor should not be landed there.
The service equipment is kind of "bullseye" where all grounding and bonding come together. Nuetrals, equipment grounds, bonding jumpers, grounding electrode conductors an dmain bonding jumpers shall be bonded together as one at this location. Anything after the service disconnect requires isolation of the nuetral.
Does this answer your question or did I just ramble?
Salt Lake City