I sailed the offshore race from Gulfport to Pensacola for many years. It was mandatory that we had the MOB pole, light and horseshoe buoy all attached. But when we tried a mob drill, it took so long to get them all off that we could be a long way from where the person went over. As a result, our routine was to attach a whistle and water activated light to a throwable cushion and have it near the helmsman, where everyone knew where it was - out of the way but not attached to anything.
If someone went over, the procedure was to throw the cushion immediately. At the same time, the helmsman was to round up. If the person overboard was unconscious or otherwise in trouble, the thrower was to jump in with the cushion and help. Otherwise, the thrower was to stay on board and keep watch. The rest of the crew was to get enough sails down to be able to control the boat under the conditions.
You want to get as close as possible, but remember that the propeller can't be turning when you're near someone in the water. Ideally, I think you want to get close and throw a line to pull them to the boat.