Yes OSMAnd does work.
Do you have SUPL enabled? Search for it in the settings. Should be enabled by default.
A-GPS speeds up getting the fix point. If you are in airplane mode, you cannot use A-GPS so getting a fix takes longer.
In the future you will be able to use network location. To improve this data around where you actually live, you can contribute to BeaconDB using the app NeoStumbler.
This means location without GPS, just with wifi, bluetooth or cell towers. Even in airplane mode! Way faster, possibly more accurate, less energy consumption, in buildings and trains etc.