I've used NLD to roll back firmware to pre-NFZ limitations on 3MP's and 1P4P. All without a problem.
To answer the OP's question, Litchi won't fly your Bird if the Bird's firmware thinks it's in a flight restricted zone. The firmware won't even arm the motors. You have to roll back the firmware.
The NLD documentation needs to be updated, but it works. There is a risk of "bricking" the operating system, and I gather that it's happened to some users, but my experience has been favorable. Just read ALL the NLD documentation & instructions first.
You may get a "firmware needs to be updated" message when you power up after rolling back the firmware. Just ignore it. Better yet, don't have your device logged onto a wifi network so it can't phone home. The only time I log my iPad4 onto the internet is to sync Litchi Hub with my local Litchi app that I fly with.