Hmmm... I think I may just have found a flaw in this cunning plan.
Whilst it's good that the app doesn't need a mobile signal (and, if using a GNSS receiver built in to the phone, there's really no reason to need a phone signal, apart from to report your every move to the ghost of Steve Jobs and his counterparts at Google), a phone signal is required to report your position to the emergency services...
Of course, you might have your iPhone with you that is unable to pick up a phone signal because its receiver is 19dB less sensitive than a Sony handset, but can still run the app and give you a position fix, but someone nearby might have a decent phone, and you could use that to call for help...
Less facetiously, many apps rely on remote compute or data services, which require a 2.5G or 3G data connection, and the coverage is much poorer than for a simple voice channel. Again, there's no need for a data connection for a phone equipped with a GNSS receiver to provide a position fix, even as OSGB, since the computation is well within the capabilities of a mobile phone. The only data service that might be required for a GNSS-equipped phone is to provide A-GPS data to give a hot fix. The receiver will acquire this data on its own if you give it time to do a cold start (as any GNSS receiver will). It may be that the reports of "my phone's GPS doesn't work unless it has a data connection" may arise from lack of understanding of the need for a cold start; their phone didn't give an immediate fix, so they assumed it wasn't working. Or it may really be poor software design of the phone, insisting on availability of A-GPS data before it will consider providing position fixes.