It's a good idea to switch the pump on for just a couple of seconds every month or so, as this will help to prevent it seizing up. Briefly running it dry like this won't cause any harm whatsoever. Vax used to recommend doing the same thing for their canister machines, which use a similar type of pump as the George.
Also, after any wet cleaning operation, get into the habit of refilling the reservoir with a little plain water and running that through the system to flush it out. This will rinse out any remaining chemical residues, which could otherwise gum up inside the pump, solution tubing or spray jets.