The RGS will act as an equipment grounding conductor. This EGC is not required since you don't have a branch circuit or feeder, but it is there.
I would use a bonding bushing to connect the #4 to the RGS.
My reasoning is that pole and its mounting will act as an earth electrode, and the RGS will either act as an earth electrode or will be connected to the building grounding electrode system. If the pole is not bonded to the RGS then you would likely have all the issues of having _separate_ grounding electrode systems in close proximity, for example concentrating 'stray voltage' from outside sources, or carrying soil currents from nearby lightning ground strikes in through one electrode and out through the other.
You already have the #4 wire, you are already installing the RGS, and a bonding bushing is cheap. I don't believe it would be required by code, but would be a cheap design decision.
-Jon