With respect to external electrical service, a RV is an appliance, receiving ground and neutral connections through the power supply connection. That's different from a structure, where the power company connects only 1-3 phases of "hot" and and connects "neutral" and "ground" for the distribution system to the earth where possible.
I don't see that it would hurt. Even if there were small potential differences between your ground rod and the power cord ground, you are not usually hooked up long enough for significant galvanic corrosion, not like a boat sitting in salt water. Your ground rod might help you detect faults in the wiring of ground at the power box.