Would it increase the isolation greatly if I replaced the "artifical" drop down ceiling with the thickest possible insulation and sheetrock?
In a nutshell, yes. However, there are caveats as usual. The noise from your childs bedroom is structural transmission, NOT airborn. Therefore, you must deal with that one from above, via carpet/padding. It will HELP emencly though to do the following also.
Between the cieling joists. You need to place TWO layers 5/8" drywall. Glue the first layer with a perimeter bead of structural adhesive. Caulk ALL joints with acoustical caulking(resiliant for years)
THEN, the second layer must be pulled up tight, either via screws or cleats, along the joists. Again, caulk all joints, with no two joints aligned. NO AIR allowed between layers.
Then pack in batt type insulation into joist cavities, a little thicker than athe depth. This will dampen the lower leaf(drywall)
Now for the REAL deal. TWO MORE layers of 5/8" drywall MUST be suspended or decoupled from the structure above, via Resiliant Channel, which is fastened to the joists, and the drywall attatched to the RC. However, fastening is method critical. If you should choose to do this, ask for fastening instructions(long explanation).
However, here is the caveats. Flanking paths via HVAC ducts, over walls between joists, pipes, electrical runs(holes) and other things of this nature, not to mention direct structural transmission from other areas upstairs, through the existing structure, can also negate this approach. To achieve high performance isolation, the "whole" is dependent on addressing all possible paths for sound transmission. Ignoring one, will effectively create a "weak link", which in essence reduces the whole to the performance of the weakest link. Doors are usually the worst offenders, but others may exist too.
fitZ