The GEC is the conductor from the Service Neutral to the Ground Electrode System (GES). The GES consists of all the various electrodes which are bonded together. At any one electrode is where the GEC stops. Past this, they are electrode bonding conductors and I don't see any splicing prohibitions on those.
The only thing you have to watch is when different size bonding wires are used. Lets say you have a #4 to a water pipe and then a #6 from there to two rods. You can't run a #4 GEC from the service to the rod because the bonding wire to the pipe is too small. Running a #4 GEC to the water pipe would be OK. Running a #4 GEC to the first rod would be OK as long as a #4 connects the first rod to the pipe. Even if there was a #6 from the first rod to the second this would still be OK.
