My initial caution arose from my experience some years back with several F-Droid apps that seemed to fail on Android 5 with GPS disabled. These apps weren't that important as I try out many F-D apps so I never bothered to confirm the fact.
Since then however with later Android versions I've not noticed one F-D app fail because GPS is disabled (for example, this phone has A. version 12 with GPS and the Play Store disabled and has 88 F-Droid apps installed and all work).
Incidentally, I occasionally install Play Store apps via Aurora Store and it's worth noting that some state that they require GPS but in fact do work without it.
I've not bothered to research why but I presume it's the reporting mechanism that's not working, the core operation of these programs being independent of GPS (presumably this would simplify programming if the programmer is also coding the program for iPhone).
I'd be most interested if anyone else has more info about this.