I think that electrolyzed alkali is more possible
Both cathode or anode is carbon electrode
In cathode, sodium ion charged.
2H+(aq) + 2e → H2(g)
In anode, hydroxide ion charged.
2OH-(aq) → H2O(l) + 1/2 O2(g) + 2e
Then we can form hydrogen.
alkali + metal ion → metal precipitate
Therefore I don't think we can form hydrogen through using metal ion.
Hope I can help u and I am right.
my chemical knowledge