It takes energy to move water up to the reservoir. The amount energy needed to take it from ground level to the reservoir would be equal to or greater than the amount it generates. Otherwise, it'd be a perpetual motion machine or an Energy-From-Nothing machine.
Sure, a battery would work, but that battery needs to be charged. It gets its charge from the hydroplant (or other source). So you'd not really be saving or making energy. It'd be a net loss in the end.
Now, if it was built for just looks and a great lawn ornament, that'd be great.