I had this problem some years ago now. The procedure itself was painless with the local anaesthetic. I had a few cleanings and after this intiial attention, the dental team measured the pockets to determine the healing that had occurred.
I have read that this disease also predisposes us to other health concerns including heart disease. As well, it keeps your breath fresher to have that bacteria that is growing in there removed.
I now go regularly to have my teeth cleaned and feel the better for it. It seems intuitively the right thing to do. I really want to keep my teeth for a very long lifetime and I believe this is the right thing to do.
There was healing for me and my mouth is now much healthier than before which contributes to my overall health.
I also think that there is less sensitivity AFTER the cleaning than before because with those pockets of bacteria in your gums there is constant irritation. By the way, I have always been very conscientious about my oral hygiene but these pockets came anyway but were due to my years of smoking many years ago.
I hope this helps. From my perspective, I would reccommend it.