Of course entire Mediterranean Sea would be completely drained
No, it wouldn't. That wasn't the idea.
The Mediterranean is a concentration basin, it's saltier because of the evaporation, which is on the order of ~1 meter a year.
The idea was to eventually lower
it by 100m or 200m , and it would take 100 or 200 years or so to complete. It's sort of like, do the math?
There were further ideas, about damming across the strait of Sicily and the Strait of Messina, with differing levels between what would then be a bisected sea. Other things too, it was a very general concept.
But as far as I know, the idea was never to drain it completely or anything close to that. The sea itself would still be largely recognizable-- Sardinia and Corsica would be a single island, Malta would be huge, the Ionian isles wouldn't be islands anymore, the Aegean would have a huge unified landmass, The Adriatic would be halved or more in surface area...
Obviously, it would still have had an enormous impacts on all sorts of things, so it's not like it's a great idea assuming it was really feasible.