Unfortunately, I'm guessing it won't have much effect this way. As I understand it, it works in conjunction with the double layers to damp the sound, turning vibrations into heat. While it may have some effect between the joists and a single layer of sheetrock, you won't get anywhere near the benefits as GG between two layers of sheetrock.
On a somewhat more personal note, in my situation, I decided to go all out on the room, staggered studs/semi-room-within-a-room construction with double sheetrock and GG, stage/riser, linacoustic/batting on walls...and now, my original budget is spent. I still need to carpet, and fabric for the walls, but as I see it, you only have one chance to build your room. Build it right the first time, and you won't have to fix it later.