Just tested this and it worked for me. I’m facing the same issue of locking the car at the beach. I use a lockbox and with the key inside it you could still open the door pressing the button on the door handle. I’ll be testing this out soon.
Cold start on an alloy engine, lean mixture to comply with emissions (high rpm) = rattle, a lot of modern (alloy) engines suffer from cold start rattle...
Just about to replace a water pump at 70k myself! At least they are reasonably priced...