The dam would still allow some water into the Mediterranean, which is why it's "only" a drop of 100m-200m in mean sea level in the Mediterranean.

Well, still the remaining water in new lower mediterranean has to go somewhere for this to be sustainable and I don't believe that just evaporation would be enough for any significant power generation capacity.

If the only outflow was was from evaporation, the salinity would keep increasing. Eventually the salt would have to be removed somehow. Perhaps some of the energy harvested at the Straits of Gibraltar could be used to exchange some of the water to keep the salinity down.