Many thanks for your responses guys.
My understanding is that the phone will definitely access the cellular network to make the initial connection to GPS satellites quicker (due to the very basic GPS hardware), which won't be an issue as I'll set it up before starting the flight.
I am not sure however if it continues downloading data through the cellular network once it has got a fix from GPS satellites. This is my main concern. I could try disabling this so that it is only receiving from GPS satellites once a fix is made, but I am concerned also that this may make the tracking less accurate.
If the phone loses its connection to GPS satellites in-flight for whatever reason, then re-establishing this would be a lot slower if, for example, flight mode was enabled.
I tried using this tracking software on the train, for around 30 minutes. It was mostly fine, but there were blips, some big, and these happened to correspond to areas where the cellular network coverage is poor (where, for example, it is not possible to even get a GPRS connection), even though the GPS signal was not lost.
pilot2bornot2b..., that was actually the exact application for this setup I was thinking of. It would be a great opportunity to use this in the debrief after my QXC.