Yes. The damage may or may not be noticeable, but it will definitely damage your hearing. Now, losing something like 1-2% of your hearing isn't a bad trade for saving your own life and the lives of your loved ones, is it? Probably not, but if you can avoid it, it is a good thing. The loss is going to likely be less than that, but you get the idea.
A gunshot indoors results in you experiencing the sound/pressure multiple times versus firing outdoors. As such, you get several impacts. With the initial blast, you get the first report to your ears, say 150 db. That alone is enough to produce mechanical damage to the ear. The second event comes from the sound reflected off of the first wall and is a first even reflection. In fact, first reflections off the walls and floor (if no carpet) will still be quite powerful. In a typical hall or living room with a tile or wood floor, you can suffer 6 first reflective events with the first shot. If your shotgun is 150 db, your reflected events could each be well over 135 db and so all six reflected events will be enough damage your hearing. So your 1 shot has produced 7 damaging events to your ears and that is assuming you don't enough up with two or more impacting you at the same time and potentially doubling the pressure when they do. After that, the sound will bounce a few more times in quick succession such that you won't even know it. You will be hit be repeated events, all travels at the speed of sound and it will likely take place within less than a quarter of a second. The events will each be less and less as the sound/pressure dies off via travel distance (multiple reflections) and by being absorbed in things such as carpeting, furniture, etc.
22-mag noted...
Note: Each increase of 6 decibels doubles the noise level
This statement is in error or at least not helpful in regard to hearing protection. They may be referring to what is interpreted by the ear such that a 6db increase sounds twice as loud. HOWEVER As noted in the original post, the pressure doubles with each increase of 3 db. So a 6 db increase would actually be a quadrupling of the pressure and it is the pressure that causes the damage.