I don't know what each individual U.S. airport's protocol is regarding firearms baggage but my experience has been sometimes it comes up the belt to the carousel and other times someone hand carries it to that area and checks the ticket numbers and my identification.
Not sure about other airlines, but American recently changed its policy for traveling with firearms. When I traveled in Feb, the ticketing agent place a tag on my bag and I had to pick it up at the baggage claim customer service area on my arrival (both ways). I think this was based on that jack A$$ in Florida who recently opened fire in the baggage claim area. While this took a little longer for me to claim my bag, I really did not mind because my bag was hand delivered to the agent and did not come out with everyone else's bags. The Agent then checked my ticket and ID before I could leave with it.