No. Salt is only used in a water softeners to clean the exhausted resin, before being flushed away. Salt is not part of the water 'softening' process and the water will not taste salty.
That said, the Department of Health recommends that you do not drink softened water as it is higher in sodium than mains water. Our installation instructions shows you how to bypass the water softener with the cold water mains feed to your Kitchen sink.