In short, no. This is because water softeners are only designed to remove build up from odorless hard water minerals and clear water iron. A common smell you may notice in your water is hydrogen sulfide. This is a rotten egg smell in well water. This requires treatment beyond a water softener.
If you're dealing with an unpleasant smell in your water supply, we recommend contacting a local water treatment specialist to help determine the best solution for your home.