A stud wall might improve 12 points with the addition of GG and drywall on one side. Presuming no flanking. There's always flanking, which will move down the achieved isolation.
- Flanking needs to be addressed. Ceiling, floors and adjacent walls.
- Decoupled construction is always a better starting point. Would require removal of the original drywall OR the introduction of a 4 1/2" air cavity.
While designing a wall based on your intuition is fine, I might suggest you stick with lab tested assemblies. There are many to choose from, and have all been tested many times by many labs. Their mileage does not vary, you might say.
Feel free to post some pics or diagram if you can. Very helpful in these situations.