I leave my S5 phone turned on most of the time.
You can even disconnect the phone, reboot it, and reconnect with the GO App, all while your Phantom is in the air. This all works best, of course, if you're flying in fully-stable GPS mode with enough battery-charge.
BTW, you DO want your phone to be on when it first establishes the home point, so your Google Maps location will be correct (it gets this through the Internet). Then, for security, you can switch into airplane mode when you start ascending. But if you forget, you should be OK.
Some issues arise because the phone can get so busy with other apps, that it causes lag. That's why airplane mode seems better.
Optimally, I've found the best compromise to be with a Samsung tablet with few apps, and to keep its WiFi on, to connect with my S5's mobile hot spot -- for the Google Maps. Very smooth operation that way, with no visual lag.