Well no I'd like to be notified if Im using my phone, and I'd like to be notified via LED or vibrate or sound or all if I choose to but I don't want my screen to turn on necessarily.
I have AOD enabled and just confirmed that, for an email notification at least, the phone did an audible and turned on the LED but did not light up the screen. Not sure if the same will occur with your apps but might be worth a try.