No problem to have both earth and arrestors - Compared to an inverter, arrestors are cheap. Most good inverters have some form of arrestors on the input, but if these get taken out, the inverter will probably shutdown till you get the MOV's replaced. However, lightning is odd stuff and can sometimes defeat the internal protection offered by an MOV by jumping elsewhere.
Here in Orkney, Scotland, installations in schools require additional arrestors to be fitted where the turbine cable enters the school, so we fit them there.
Bear in mind that the arrestor also needs a good earth - It cannot sink a lightning impulse into fresh air! So it needs to have a good, low resistance connection to earth, otherwise it will be worthless.
12mm rod is fairly typical (5/8" is common in UK) so you cannot predict the final resistance from earth rod diameter alone. The soil resistivity on its own has a much greater effect! I remember about 10 years ago, trying to get a good earth for a 1.3 MW turbine up here in Orkney on the infamous Burgar Hill. We drove down 5/8" rods coupled together to a depth of 9 or 10 feet below the bottom of the foundation using a power driver (the rock was too hard for hand driving!), which, by the time the foundation was backfilled, would have put the bottom of the rods about 17 feet down. We managed to get 3 sets of rods down between cracks in the rock, hoping that they would find something moist down there. When we coupled the 3 sets together and tested the resulting resiatance we had over 150 ohms! Hopeless, when our target was under 10 ohms!
So we abandoned those and installed what are now more conventional horizontal electrodes, and I don't think we have driven an earth rod since! Everything we do now, whether individual small 6 kW turbines, or windfarms, uses horizontal electrodes. Takes a lot more copper, but gives more predictable results.
Good luck with the "drive and test" method! If you have access to an earth tester, and it is capable of testing soil resistivity (4 terminal), you may want to try that first to see if 1 are 2 rods are going to give anything like the target you are looking for. If not, then bashing copper into the ground is a bit of a waste of time (and copper!)