Android: you are able to switch off mobile networking while using GPS
You can do, yes. If I turn off the mobile networking on the Android device I use at work whilst sitting at my desk its error goes from sometimes less than a hundred metres to putting me in a field 2km from the office.
It does better outdoors with a decent view of the sky, provided you switch it on and stand still for 15 minutes before expecting much in the way of reasonable results (that's with wi-fi and phone network both turned off). Then the error can go down to single figures of metres, which is fine for VMC navigation.