There is an Israeli carry technique that specifies carrying a semi-auto pistol without a round in the chamber. In this technique, the pistol is drawn with the right hand, tilted sideways with the slide to the left, where it is grasped by the left hand and the action is cycled while the pistol remains sideways.
If a quick shot is required, the shot is made from the sideways position. I believe I have a video of this technique being demonstrated. I have heard that this video might have been Hollywood's inspiration.
I also recently saw a picture of a Revolutionary War soldier shooting an enemy soldier at very close range using this hold.
In any case, I'd believe I'd get a moral boost if I faced an opponent and saw them using this grip.