This sounds off. Conventional ships experience drag when they try to go forward and there's a bunch of water in the way. When they shove that water out of the way, it has to go somewhere else, and meanwhile some other water has to flow into the space where the ship used to be. That motion of the water generates the wake.
But all of that applies just as well to submarines moving below the surface of the sea, or cars driving around within the atmosphere. If a car passes by you, you'll feel wind blowing after it. That is the car's wake. And when a submarine tries to move underwater, it runs into exactly the same problem as the surface ship -- there's a bunch of water in the way. How can it possibly move without generating a wake?