The answer is currently NO. This is a list of functions that you will need your DJI app for, thanks to TriBar who is one of our Forum Leaders.
You need the DJI App for:
-Activating a new drone.
-Firmare updates.
-Unlocking No-Fly-Zones
-Calibrating (if needed) the IMU.
-(Re)Naming the drone.
-Some MC settings.
-Some obstacle avoidance settings.
-Gain & Expo tuning.
-Some Remote controller settings:
-Stick Mode
-5D button customization.
-Remote controller calibration.
-Remote controller linking.
-Read the Sensors State.
-Image transmission settings.
-Aircraft battery settings.
-Payload setting.
-Beginner Mode.
-…
Perhaps others can complement this list.
The main goal of Litchi is to add functionality, NOT to replace the DJI App.