Yes, and it would improve the taste. If you like San Pellegrino, you can get a similar taste at much lower cost by adding "Burton Salts" (a blend of salts meant to imitate the water of Burton on Trent, which is famously well suited for making pale ales, widely available from brewing suppliers) to soft water.
And people have made spreadsheets to help with cloning specific mineral waters with the exact blend of salts, e.g.:
