I would never put my drone in checked bags. I have never had issues having my drone in my carry on. In fact the TSA was far more concerned about my camera than the drone, they never even glanced at it.
I have flown My MP1 several times without a phone or iPad, yes you have to have the drone close so you can see it, but the times I have flown I wasn't going far anyway.
The app has nothing to do with range, the controller does, I have flown my MP1 just as far without my phone, as with my phone. Again the phone is just a visual aid nothing to do with the drone.