Will adding a water softener to a house with hard water loosen / dissolve existing sediment?
Funny Enough, I also have a Water Softener that has been working strong for 10 years. When we first bought it, I called Whirlpool about the same question. Because In Southern California, we also had a long stretch of time where we were getting very hard water. 

I spoke to a rep from Whirlpool regarding this very question. 'Could the water softener clean the pipes in the house. Or was there specific kinds of pellets, I could use in order to help make that happen.

And the answer is No.

What you have to understand is a Water Softener does 1 job, it removes calcium from your water. There are also pellets that prevent rust within your machine. But not rust in your pipes.

The machine is what removes the calcium from your water. In order to maintain the Water Softener to keep it functioning properly, you need to clean the resin beads that attach themselves to the calcium. The salt pellets that you dump in the Water Softener is what does the cleaning. The salt is what cleans the resin beads. That's why you don't taste salt out of your home faucets. 

Is it possible to clean your pipes in a different way? Possibly, but it can't be done with a Water Softener.