That is exactly right the way you described it in the OP.
I thought I heard you went to the rod first, Even then it would be OK as long as you had the #4 or whatever 250.66 calls (to bond the water pipe)
The GEC is the first connection to an electrode. everything is a bonding jumper.

From the handbook

[Linked Image from gfretwell.com]

Greg Fretwell