On a general side of it. You don't actually need it since your character 'flinches' and 'health bar' goes down.
Both of which are FAR better indicators of damage than off putting hitsound.
and the most common battle is Machine Gun vs Machine Gun Which means high rate of fire of receiving and hitting bullets. Which means Normal Hitsound+This = Earrape/Annoying Sound that ruins gameplay. So did you really take that into consideration before posting this?
But then it must also be taken into the consideration that it will be useful for spotting bugs,glitches and rate of fire committed by the enemy.
So yeah good idea in that perspective imo. But I think a real time damage indicator is far better than that.