Unless the spy app has the ability to activate a transmission at a set interval, which is out there.Only over the air. Anyone getting his hands on your phone can still hack it. Any app written to "phone home" with your data will still do it once you turn the radios on again.
But while airplane mode is on and you're holding the phone, no one can get into it.
Unless the spy app has the ability to activate a transmission at a set interval, which is out there.
Either a Faraday cage or take out the battery is the 100 %safe bet.