Well the intended purpose was never draining the Mediterranean Sea completely and the scenario you present seem to have just this in mind. The goal of Atlantropa in XXI century would be neither energy production nor joining Europe with Africa. If anything it would be preventing sea level rise.
But you'd still be diminishing the volume of the Mediterranean by a large margin, and draining the Mediterranean Sea to the extent proposed, lowering its surface elevation by 200m (or more), would still undoubtedly be enough to triggering a renewed Messinian salinity crisis. As winds blew across the "Mediterranean Sink", they would heat or cool adiabatically with altitude, with a dry adiabatic lapse rate of around 10°C (18°F) per kilometer of elevation- in other words, the new surface temperature of the Mediterranean, and the temperature of the winds which would blow across it, would be roughly 2°C hotter than it is now, as a result of the new 'Mediterranean Depression' being 200m below sea level. This would rapidly increase the rate of evaporation and the process of salination, which would only be exacerbated by the fact that you'd no longer have any outflows. Today, the evaporation from the Mediterranean Sea supplies moisture that falls in frontal storms, but evaporation still greatly exceeds precipitation and river runoff in the Mediterranean, a fact that is central to the water circulation within the basin. Evaporation is especially high in its eastern half, causing the water level to decrease and salinity to increase eastward with this evaporation.
It's already one of the saltiest bodies of water in the world for this reason, with up to 40% salinity in the East along the coasts of the Levant, similar to that of the Red Sea- and by lowering the basin by 200m, you'd increase temperatures, salinity and dessification to markedly higher levels than those of the Read Sea today. As a result, the Mediterranean climate that we associate with Italy, Greece, and the Levant would be limited to the west of the Iberian Peninsula and the western Maghreb; climates throughout the central and eastern basin of the Mediterranean, and surrounding regions to the north and east, would be markedly drier, even above modern sea level. The eastern Alps, the Balkans, and the Hungarian plain would also be much drier than they are today, even if the westerlies prevailed as they do now. In effect, if you did this, then you'd be extending the Eurasian Steppes ecoregion all the way along the Alps and the Pyrenees right to the sea, and you'd be changing the climate of the entirety of Europe south of the Alps to match those of Iran and Central Asia. And this amount of disastrous localized warming and climate change in the Mediterranean basin, equivalent to that projected as a result of global warming over the course of the entirety of the 21st century, would take place over the course of just five or ten years- only a tenth to a twentieth of the timeframe. Result? Apocalyptic.