Regarding has2be's statement that screwing the two pieces of birch ply together will defeat the isolation provided by the constrained layer damping placed between them, that layer of damping material is put there not to provide isolation for the turntable, but to absorb and dissipate the resonances of the plywood itself. Green Glue, ASC Wall Damp, and EAR Isodamp is too thin to provide any isolation. It is the springs, roller bearings, Herbies feet, or Seismic Pods (or even slightly inflated inner tube) placed under the shelf that provides isolation, not the constrained layer damping.
No harm in trying the two pieces of ply both screwed together and not, though. However, Green Glue doesn't completely harden, which would allow the two pieces of ply to slide around in relation to each other a little. ASC Wall Damp is tacky enough to keep the pieces of ply from sliding against each other, but EAR Isodamp isn't; if using it, the two pieces of ply will have to be attached to each other in some fashion, ergo my suggestion of screws. Since the ply/constrained layer/ply construction should function as a single unit, you actually WANT the two pieces of ply to act as one. The reason for using two is to increase the stiffness of the shelf, and to allow the installation of the constrained layer damping, to make the shelf less resonant.
If you want a layer of isolation-proving material between two outer layers of stiff material, the Symposium shelves are the way to go. They have outer layers of stainless steel, with a thick layer of foam between them, to provide isolation. Symposium makes a version of their shelf with springs attached to the bottom, specifically for turntables. That model is relatively modestly-priced, around $350-$400 I believe.
