It seems that there are about three ways of adding hydrogen to water. One is bubbling H2 under pressure, one is electrolysis plus H2 (which would result in additional ions), and one is adding a bar of magnesium to, I guess bind or split more hydrogen gas molecules into elemental hydrogen.

So, it’s not clear to me if there is truly diatomic molecular hydrogen or hydrogen ions, but considering the solubility of H2 in water, I would guess if there were am effect it would be the latter.