I have just verified that the Steam Controller works well with the game out of the box without any changes. In general the game should have partial support for Steam Input devices in the same manner that it does for Xbox and PlayStation controllers. Most of the actions can be rebinded as desired.
The only issue I noticed was that the parking brake on aircrafts is very sensitive on the Steam Controller. Usually you can hold down the left bumper and press the B button to toggle the parking brake, on the Steam Controller this seems to only work if you hold down B and then quickly tap the left bumper instead of holding it from the start. You may be able to tweak this behavior if desired, but by default it will be a little fragile since it was never designed for this device.
Note: Apparently the parking break works fine for some.
Other than that you can use the Steam Controllers the same way the game is supported on the Steam Deck! I think that is pretty cool.
Enjoy!
-Revmatek