Its all up to you, it won't hurt the grill either way.
Here is what the cool down was designed to do.
Burn most all the remaining pellets from the pot then dump any smoldering ones from the tube and eventually shut off automatically (max 20 min). This leaves a cleaner fire pot and fresh start the next time you light the grill.
If you don't use the cool down the pellets that were on fire in the pot will smolder a long time and leave behind more ash in the pot.
Not to mention, the cool-down mode is especially nice to help get the grill cooled down a little quicker to put it away or load it up on a trailer after catering a BBQ.
If you have the time I would always use the cool down mode. As others have mentioned it really helps to keep the burn pot and auger tube cleaner for a better start up next time.