Arduinos are a teaching platform, not exactly designed to be robust. An Arduino board will probably do well for prototyping on your bench, but may cause problems when you try to take it to the air (mostly mechanical).
You'd be using the bare microcontroller soldered firmly on your own PCB to do the control of the helicopter, together with all the required extra hardware for protection of the inputs, control of the outputs, etc.
Other than that, I don't see any real issues, provided the processor itself is powerful and fast enough to handle whatever it has to do. It's commonly used in building model quadcopters so that should work for a full scale one which is probably actually easier to fly (it's weight and slower reaction to changes make that you have more time to react and make corrections - but doing it wrong has more serious consequences).
So that begs the question: did you ever build and fly a model/toy size quadcopter?