I travel frequently and always have a weapon, so I have encountered many many different scenarios and I am quite sure that I will continue to encounter new and different things. On the whole, it is pretty standard, but I find it all starts with the first agent that you encounter and much relies upon their knowledge and experience in dealing with firearms in baggage. Newer agents with less experience will need more patience, which was my last scenario about 3 weeks ago. I will also make an assumption, purely speculative, that agents own personal bias will guide their actions. The amount of inspection or curiosity with the ticket agent may vary. Some don't care to see anything, will ask quick questions, fill out, or let you fill out your firearms tag for the luggage and move on. Others may want to see the unloaded weapon, check your pistol box, if not in a hard locking gun type of case (pelican or similar), ensure there is no ammo present, etc...
On this last trip on the outbound leg, I had an agent flat out say that this was her first time doing a firearm check-in. No problem, I helped walk her through things, once she verified something with a supervisor. She also asked about ammo as she was reading the rules directly off the computer. I said, yes, in separate luggage, factory packaging, less than 11 pounds. She actually asked to weigh the ammo, but then I pulled out a single box and she felt a little embarrassed. I told her not to worry.
On the outbound leg, I met with the TSA agent at the "oversized bag" check in area. I use my own locks. He did not ask to have the case opened, sometimes they do. He swiped the Hardigg got the reading and said, have a good trip and turned the bag over to the baggage guy who was also waiting. Slow day. Upon picking up the bags, they were both at the oversized area, no one immediately around. I picked up the two hard cases looked around, then walked away. A young lady came running up and actually addressed me by Mr. xxxxxx and asked very politely to see my baggage claim tickets. I thanked her for keeping an eye on my bags and not letting just anyone walk away with them. She felt good about that as she seemed a bit nervous about stopping me. No oversized charges.
On the return leg, very cool ticket agent. Breezed me right through. He did see inside my case as I put in the firearm card and he said, "cool M4". Of course this struck up a conversation. Real cool guy, too bad they all didn't go down like that. Bag went behind closed doors to TSA. When this occurs, they may or may not ask to open the case, just depends. They did ask to have it opened. I will also note that my other Pelican case, did not have a live firearm, no ammo, but did have my gear with mags and holsters a blue gun and a SIRT pistol. So TSA did open it for inspection also. You must hang out, until the bag passes TSA or they will have to hunt you down, or open the bag on their own.
I will note that when I hit HNL baggage area, the bags came out while I was there waiting. They were brought in via the "backdoor" by an airline baggage handler and placed by the "roped" oversize area, just outside the door. I walked up, picked up the cases and left. No one was around.
IME it is like Forrest Gump says, "its like a box of chocolates..."