I fly MDW-LAS often, and due to the flight frequency on that route, I often check in before earlier flights have left. Last year, my bag arrived before I did several times. Once, I was delayed and my bag had arrived back at MDW at least 5 hours before I did. Now, the first thing I do when I arrive at baggage claim is check the bag holding areas to see if mine is already there.
As I understand the domestic security rules, a passenger cannot choose to separate himself from his bag, but the airline can choose to do so.