I don't think so. Think about a tube of silicone for instance. In that case the "cone" would be the plunger thing you push on to make the silicone come out. No matter what shape that plunger thing is (cone or flat or multi cones with a ported chamber in between) the same amount of silicone is going to come out for a given input stimulus (like a squeeze on the trigger).
Sd is cross sectional area of the diaphragm, regardless of the diaphragm geometry, regardless of whether you you make a cone with an internal chamber inside of it.
The air inside the cavity is a static load, it's not going to do anything, certianly not increase Sd. The speculations about high velocities coming through the outer cone center hole are wrong - the two cones are connected and moving back and forth together. There's going to be no air flowing in and out of the cavity, the cavity and it's air load will not pressurize and depressurize. In short, the cavity is going to do absolutely nothing but add unnecessary weight.
I welcome you to refute this, but please back up your statements with... anything really.