Surely they already do that. The trick is not knowing whether an abnormal input is a drill or not, or at least not knowing when a drill might happen. All these issues have been solved in the military a long time ago.
Knowing when a drill might happen improves alertness during the drill period only. Drills do develop and maintain the skills required to respond to a non-standard situation.
There might be other ways—you could at least do it on simulators, or even on training flights (with no passengers).
Surely they already do that. The trick is not knowing whether an abnormal input is a drill or not, or at least not knowing when a drill might happen. All these issues have been solved in the military a long time ago.
Knowing when a drill might happen improves alertness during the drill period only. Drills do develop and maintain the skills required to respond to a non-standard situation.