When hanging two layers of drywall, can the first layer be hung with the facing to the studs?
Green Glue does stipulate to be used between rigid layers. However, even the beveled edge of the drywall meets this definition.

The edge of the drywall is beveled so that the mud and tape when finished doesn't create a "hump" in the wall at the seam. If you don't mount the drywall with the beveling in the right direction (towards the room) then you will notice all the seams.

Let me preface by saying that I think the green glue installation will be just fine even against the beveled edge of the layer beneath but if you still want to make sure the surfaces are smoothly mated then you should install the inner layer backwards and the front-layer correctly.

That is, the stud-attached layer has the beveled side facing the studs. This leaves the rough edge (without bevel) facing the room. Then the finish layer adhered its rough side to the wall... thus the finished, beveled side faces the room.

On a side-note, are you also using low-density soundbard and insulating the walls between the framing members?