That's actually an interesting question, and the manual (at least mine) doesn't specifically say:
"1. Press and hold the Power Button for three seconds to turn the unit off. The grill will begin its automatic cool-down cycle. The auger system will stop feeding fuel, the flame will burn out, and the fan will continue to run until the cool-down cycle is complete."
I could be wrong, but I think the main goal during shutdown is to burn off any pellets in the firepot, to help prevent a fire from running up the auger into the hopper. So, during shutdown, the fan runs but the auger stops feeding fuel. I always thought that was a timed cycle, but the manual implies temperature control. Having the lid open or closed probably is splitting hairs, but in some conditions this old boy scout can see where the fan might control the burn off better with the lid closed.