If the drone has not been activated then YES.
If the drone has previously activated then it probably can be flown with out the app being active but height and distance may be severely restricted and, in some cases, you will probably be unable to fly it at all. There may be messages 'waiting' for your response before the drone can be flown, without the App you won't see those messages and will not be able to respond to them.
Besides, if you want full control of the drone then the app is needed.
I would have thought that the app would be already on the controller, is it not?