A septic tank breaks the waste into three categories: 1) scum that floats to the top, 2) waste that settles to the bottom and is eaten by bacteria and decomposes the solids, and 3) effluent (liquid) that is in the middle and runs out to the drainfield.
There is a delicate balance in your septic tank to keep the bacteria healthy and working. When you use too much soap, Clorox, etc. it will kill the bacteria and the septic tank will stop working. Adding a treatment neutralizes the soap, etc. and keeps the bacteria healthy.
Your dry well does not have this layer of waste and bacteria. Rather, the waste is scattered throughout the well. So, no, adding a treatment like Rid-x will not help.