I'm going to throw a fly in the ointment.
Grounding the radial plate might..... or might NOT...... improve the RF ground.
If you have a sparse elevated counterpoise or insulated radial system, grounding the radials can actually make the ground system worse.
If you have a good system, it makes no difference at all in anything for signal and will barely change lightning behavior, and will not affect static or charge buildup at all.
I'm working on a counterpoise page:http://www.w8ji.com/counterpoise_systems.htm
but it is very involved and is incomplete. If you read what is there so far, it clearly illustrates problems with earth connections when ground systems are small, or truncated.
If you have a reasonable size earth-based radial system, with radials in, on, or in contact with earth, that small addition won't do anything at all one way or another performance or safety wise, and neither will a ground rod.
If you have a smaller ground system, the only accurate answer is "it depends".
If you install 20 radials 25 feet long on the earth or in the earth, a rod ground connection is totally meaningless for RF. An earth rod might be a slight advantage for lightning and electrical safety, because you have insulated wire. It won't reduce static, and it won't reduce chances of a lightning strike. You also might speed physical deterioration of the mounting pole with electrolysis by tying it in, if the pole metal choice and other factors are wrong.
If you have a smaller ground system, especially one isolated from earth, a ground connection can reduce performance.
Frankly though, with a 32 foot vertical and a remote tuner behind a long length of coax, worries about efficiency on bands other than 40 meters are relatively minor. The antenna system will not be all that efficient because of matching method losses, and on 15 meters and higher a 32 foot tall vertical wastes a lot of energy at high angles. This does not mean you will not be happy or not make contacts, I'm just pointing out losses in the ground system are not as important because there are so many other additional losses.
The popular monopole one-length-fits-all non-trap verticals are not high performance systems, they are just easy antenna to build.