For engaging a reactive threat's torso inside of five yards (fifteen feet), you do not need to use the sights at all. In fact, you are better off simply raising the pistol into the line of sight, pointing it at the chest, and pressing until he drops to the ground. We will wait for the collective gasps of the "sights all the time" tribe to subside, and so they can strike my name from the Raven's Book Of Life before we continue.
Alright, all joking aside, when the problem calls for point shooting, you point shoot and the type of sights on the weapon are irrelevant. But when you do need extra refinement...which happens often enough, the sights are of great importance as they help you refine alignment as well as index carefully on target.
So lets set down some points:
The dot does not work WITH the sights. It works independently of the sights.
Think of the iron sights and the red dot like two distinct and separate sighting systems. You do not need one in evidence to use the other. With reference to the dot - as long as the dot is on the desired area of the target you wish to hit, you will in fact hit that target area - regardless of where the dot is in relation to the iron sights.
The parallax-free nature of these red dot sights enables you to make extremely accurate shots without the dot needing to be centered in the glass. The weapon may be offset from your line of sight. You are able to keep your visual focus on the threat/target since the dot and target are in the same focal plane of vision.
This greatly improves your ability to return fire from cover, fire at speed, fire on the move at a moving or stationary target, as well as shooting accurately from disadvantaged positions.
All of these "Red Dot Sight Pictures" are acceptable and as long as the dot is on the target spot you wish to hit, you will hit that target spot.