I think the EGC/GEC can't share only because a GEC is to be unspliced. How do you get it to the pipe unspliced without violating a rule?
If the water pipe is just being bonded and is not a ground electrode, what the OP wants to do may be legal. But he'd have to verify that the water pipe outside is non-metallic. If the pipe is just being bonded, I know of no issues for number of splices, wire routing/grouping/sharing, etc that would prevent this. It does have to be large enough the whole length though (and #4 cu would be right).