No, a softener will not remove the sulphur odor. The odor is a gas and has to be let out of the water before getting to your faucets.
We do this with an air pump and a galvanized tank under pressure. Some people use aerators. I don't like them because they are unsanitary. A lot of treatment guys use chlorinators to kill the odor. I personally don't like injecting chlorine into my plumbing. It's hard on everything it comes into contact with.
There are a few majic filters on the Internet also. You might want to take them with a grain of salt.