I doubt it will hurt to do so, and it might make some feel better not to have the #4 wire just hanging.
I do not buy into any of the presumed bad things that might happen. For instance, I see no way for lightning current to flow from the #4 wire to the RGS UNLESS they are connected together.
I have personally encountered a phone line that appeared to have been destroyed by having two separate grounding electrodes.
The phone line entered the building via a telco block with a wire to a random ground rod.
The electrical system was properly grounded via ground rods on the other side of the building.
The phone was not working.
Upon investigation a random stretch of wire near the floor well inside the building was surrounded by a series of scorch marks along the wall, with the copper conductor broken up and coming out as spikes along the wire at each scorch mark.
There was no evidence of a lightning strike on the building.
The building was located 'near' a set of high voltage transmission lines.
My _guess_ is that a nearby strike caused a difference of potential between the two ground electrodes.
The whole point is that if current is trying to flow between two ground electrodes, you _want_ it to flow through a made conductor, rather than creating a significant potential difference.
-Jon