Since, according to Plato (the only surviving source of that story) Atlantis was destroyed thousands of years before this, no.
Faults are varied in type. The usual are strike slip faults. This is a sideways action. The two sides of the fault slip sideways, horizontally.
The really ugly ones that generate the huge numbers are subduction faults. With these, the two sides of the fault move vertically, with one plate pushed down beneath the other. This is what generated the huge actions in Indonesia in 2004 that stretched to countries hundreds of miles away. Ditto the 9.2 off the coast near Anchorage in the 1960s.
Those were subduction events. The one lurking off the coast of Seattle will also be a subduction event.
But the eastern Med is not subduction. There is some evidence of subduction in the western Med, but not eastern.
So . . . story probably bogus. That big event is usually ascribed to the Thera volcano.