In Egypt you already have long stretches of the Indian Ocean coast without mangrove or any other vegetation.
But the problem with mangroves is that these grow more or less in a belt between tropics (~ <= 25degs latitudes), require some rainfall and salinity not exceeding some limits.
I am not aware of any patch of mangroves on the mediterranean coast.
Last but not least, these trees are adopted to tides or estuaries with lower salinity.
You will not reproduce such conditions in an oversized saharan Dead Sea.
Wasn't there even a plan that involved using up the nuclear stockpile to 'dig' a channel and drain the Mediterranean Sea? Of course there might be some opposition to that currently.
Of course the evaporation might raise the salinity above what they could handle. Perhaps a monthly flush out somehow?