No. You should only distribute salt into the main salt basin of the softener.
If there is a large amount of salt in the brinewell, it will likely melt together and deter the float assembly from working properly. In this case follow our Cleaning the Salt Tank and Brinewell article.
If you accidently drop a few pellets or crystals into the brinewell, we recommend pouring 2-3 cups of hot water into the well to dissolve the salt.