Arma 3 doesn't support controller to be turned on after the game was started. You should not be forced to have the controller active from the start.
Sometimes i wish to turn on my xbone elite controller because i'll have to drive in the mission i am currently, it wasn't planned so i didn't started my controller, but even if i turn it on the game won't see it until i restart the game..
Same goes for an HOTAS or joystick, sometimes you have to fly even if it was not your job and you have to deal with mouse/keyboard only.