I haven't noticed anything major. I'm sure there's some scientific studies out there though.
However, the original carbonated water was that of mineral springs, which have natural minerals and hardness, usually due to calcium carbonate. Something about how calcium carbonate dissolves under pressure and carbonation.
many waters back in the soda jerk age and even now use distilled water and add specific amounts of various minerals and salts to create mineral water (which has hardness due to the additions).
In regards to these, I'd say that it's going to be pretty negligible. (You might use more, or less, co2 to carbonate perhaps, but it would not likely be a significant amount).
Secondary: GF Czech Lager
Waiting to be kegged, Italian Primitivo
Kegged&Ready: GF Orange&Coriander, GF Honey Lager, GF chocolate ale, GF English ale, Island mist (zinfandel), Island mist (cbry malbec).
Bottled: Infected Mead, Dry Hard ciders, Accidental Sorghumwine, various unnamed.