The GA mod uses offline flightplans, the same as AIG when using it’s injected traffic with their traffic controller and with using FSLTL with it’s injector that pulls them and makes them on the fly. The difference being that AIG-TC and FSLTL injector “inject” their flightplans into the sim and the GA mod doesn’t (it uses a traffic.bgl file).
If you use MSFS live traffic then MSFS will pull from liveries you have in the community folder (say AIG liveries, FSLTL liveries) that match the airline codes and use those liveries. It’s not using the flightplans (in MSFS live traffic mode), just pulling liveries that match airplane codes. MSFS live traffic does not use traditional flightplans (MSFS injects the live traffic itself) whereas offline traffic does use traditional flightplans.
Injected flightplans (such as AIG-TC or FSLTL injector) may or may not work along with MSFS Live AI (I’m not sure on that) even though they were not designed to be used that way. The GA Mod doesn’t use an injector though, it uses an actual flightplan file (the same as MSFS stock offline traffic does) and as such, will only work when MSFS is in offline traffic mode.