no, in many experiences the locks on the pistol case itself cannot be tsa approved, i.e. only you can have the key or combo to the locks, tsa locks can be unlocked by someone with the appropriate key. in any event i always travel with extra sufficient tsa and non-tsa locks on me to account for any vagaries. know laws at departure/transit/arrival airports,
https://www.handgunlaw.us/
i very often fly with declared & checked pistols, including to/from/through ord, phl, san, except never/never to/from/through ewr, lga, jfk, bos. ensure that your pistol case is hardsided and has two locking points (pelican cases are generally gtg). apply non-tsa locks to the pistol case, and in then place this pistol case inside some regular airline bag with a tsa lock applied. pistols and mags must be unloaded, ammo in factory box or plastic purpose-built ammo case only, all inside pistol case. check in early and declare to airline staff. follow their instructions and you should be retrieving this specially redtagged checked bag not on carousel but at airline’s own baggage service desk. be patient, some airline staff are unsure and occasionally upset with firearms, others are a sheer pleasure and make small talk about their own pieces.