No, you don't use a ground rod for anything unless it's bonded to the equipment ground at the service.
You better figure out what this lead is for. If it's connected to the ground on the supply then the machine is already grounded and another ground by this lead pointless.
Are these machines new? If yes what does the manual say? Do you have a manual? If they are used could these leads have been installed by the previous owner for some reason? Could these leads be used to ground the spray gun that is being cleaned rather than what you assume?
-Hal
