Not for drinking filtered water, because the minerals are dissolved in the water. You do, however, lose minerals from drinking softened water and bathing in it (technically, you don’t 'lose' them from it so much as be deprived of normal mineralization of 'hard' water (where we get a lot of magnesium). Filters generally remove organic contaminants, sediment particles and bacteria. Some people have softened water in the whole house, some only on the hot side. Sometimes, a peroxide injection system helps to oxidize dissolved contaminants so they can be filtered. There are a lot of ways to treat water and knowing how yours is treated is helpful to know what you should do to compensate.