The drone is still in GPS mode in Sport Mode - yes!
It doesn’t kill the application - only the mission that’s been uploaded to the drone by Litchi.
The uploaded mission runs totally autonomously from the app and the RC once initiated.
I tend to use the pause button to stop the mission.
Selecting Sport Mode, or pressing Pause, similarly stops any of the DJI built in things - tracking/POI/Pano, etc … so it’s doing nothing different to Litchi than it does to its own gizmos.