We recently moved into a semi-detached and my better-half is disturbed by airborne and impact noise from next door. Long story short, we've had an engineer, an architect and a sound-proofing specialist inspect our unit and make recommendations.
Kel, based on my understanding of what has been recommended to us, it sounds like your plan could result in at least a 50% reduction. Your approach should address both airborne (voice, music from speakers, etc.) and structural (impact) noise to some degree. We are proceeding in a first step with blown cellulose insulation to fill the gap between the drywall and the cinder block dividing wall on our second floor and in the attic. The sound-proofing specialist expects this to yield a 50-60% drop in airborne noise.
If that is sufficient for my wife to be able to sleep without being woken, we will probably stop there. If not, the next step will be a false wall. The key to the false wall, the second layer of drywall as you have described it in your plan, is to ensure that the studs do not come into contact with the first layer of drywall. Leaving a 1" gap between the first drywall and the studs for the second drywall is ideal.
Best of luck to you.