Assuming your light is 100-200 lumens, you should be fine for interior HD distnaces.
Outside is another matter. Most red dot sights work by reflected a led dot off of a coating on the inside of a lens, sort of like mirrored sunglasses. That coating is sufficient to reflect the dot to your eye, but also stops the transmission of some light through the optic. As such, regular red dot optics tend to look prematurely or overly dark in low light situations...such as at dusk where you notice that you can see a distant object much bettre with your naked eye than by looking through the optic. So it has a sort of "dark optic" effect. Eotech's holosight does not have this issue.
So you need to be able to overcome the light transmission deficit by having a bright light. Different red dots coatings and size will affect your ability to see through them. The smaller the tube holding the dot, the less light that will pass through it, as in photography with aperatures.
I have an Aimpoint Micro T-1 on a couple of long guns. Using a 200 lumen (manufacturer rated) Olight Warrior flashllight, I found that I could properly and quickly identify animals out to 50 yards or so. At 70-75 yards, identifications were difficult, sometimes not possible, and took much longer. The earthtones of deer, coyotes, etc. would not reflect much of the flashlight light back sufficiently to overcome the coating in the lens, though I could identify the animals with my naked eye at that range. Of course more reflective colors or surfaces were able to be seen and identified at greater distances. I seem to recall that I had no problem identifying steel silhouette targets painted white out to nearly 100 yards. You probably cannot count on your possible intruder to wear clothing that is highly reflective.
So inside your home, you should probably be fine with just about any red dot optic and a decent light. Where you will be hindered is outside and at distances well beyond most defensive shootings.
You should be made aware also that a bright light reflecting off white walls at short range can wash out the red dot much like daylight sunshine can. That means that you may need to run your dot at a high brightness level. When you run a red dot on higher brightness levels, you will likely have "retical bloom." This means that your 2 MOA dot or 4 MOA will be much larger than their stated size. Should you need to defend yourself outside, at night, and at greater ranges, the bright reticle is a hinderance. Not only will the reticle be so much larger, the high brightness will be such a contrast to the darkness that it may be difficult to see things beyond the dot. As noted above, an auto adjusting red dot would solve these problems.
Before you buy a sight, verify first that the sight is capable of handling the recoil of the shotgun. If it isn't capable, you may find the sight breaking internally. You may lose the red dot if the parts directing the LED fail entirely. You may find the parts directing the LED have simply have been knocked out of proper alignment and the red dot seen anywhere on the front lens other than its proper center location. The sight may fail entirely if the circuitry is damaged by the recoil.
