Here are the TSA rules for guns.
The two important ones are:
The container must be locked. A locked container is defined as one that completely secures the firearm from access by anyone other than you. Cases that can be pulled open with little effort do not meet this criterion.
We recommend that you provide the key or combination to the security officer if he or she needs to open the container. You should remain present during screening to take the key back after the container is cleared. If you are not present and the security officer must open the container, we or the airline will make a reasonable attempt to contact you. If we can't contact you, the container will not be placed on the plane. Federal regulations prohibit unlocked gun cases (or cases with broken locks) on aircraft.
If you put a TSA lock on your gun case you are breaking the first rule up there. Don't to that. Do not make yourself a criminal just to be helpful to the TSA or the airlines. Plus TSA locks can be broken open by a 6 year old with a pair of cheap pliars. Not very secure.
Of course the issue will always be that TSA does a horrible job of training their employees, and an even worse job of screening who they hire. Also to keep the terrorist confused they change their operational procedures daily or airport by airport, so some days there are new screening measures in place and when you change flights you will find a whole new world at the screening area. However, none of these changes should effect your checked baggage. Now the bag handlers that work for the airlines are a hole other kettle of fish and there is no telling what goes through their minds.
For east coast travel I recommend never flying through NYC or NJ. The port authority cops have some serious miss understandings about their own gun laws and if you get forced to lay over or delayed and are standing around the airport with a gun case you could be totally screwed by the little Hitlers that make up the port authority police force.