I flew Air France LAX-CDG, checked in my bag at Tom Bradley, then took a glance at Tom Bradley TSA and it looked like the disaster zone it normally is at around 8pm so I decided to walk over to to the Delta One check in area for the sole purpose of using their TSA checkpoint. Yes it adds walking distance but it was worth it to be the only person in a TSA checkpoint.
They let me in with no issue at all, but they did ask if I had already checked in my bags with Air France because Delta is not able to check in bags for any carrier other than Delta (although I believe Delta handles check in for Aeromexico at LAX). If you have checked bags and are flying AF/KL/KE/VS you will need to check them in at the operating carrier counter before you can use their TSA checkpoint. Or if you are carry on only then you can go directly here.
After TSA you proceed directly to the sky club, I ended up leaving immediately and using the T3-TBIT connector to go to the One World lounge in TBIT because I prefer the food in the One World lounge compared to the sky club (AF/KL contracts with the Qantas business lounge at LAX because the KE sky team lounge at LAX is a dump) . The walkway to Tom Bradley puts you directly at the One World lounge entrance, so it's pretty convenient when flying AF/KL.