Any foam or insulation under wood would dampen sound. Sound barrier would be best, softer would be quieter (or dense enough to deaden.)
Wood, even covered, reflects more sound up than foam (you know many skip the wood now, going to foam up to 3" thick). But screwing track on foam is more like pinning it down. Ho folks use caulk a lot to glue track on foam. It depends on your use, and expectations.
On traditional layouts, sounds reflect up and telegraph into the wood, traveling to the flat underside, to make lots of noise in that direction too. Foam will help absorb the sounds facing the floor, even if glued there after the fact.
But any screws solidly attaching top trough to the frame work will transmit sound so caulk/glue is in order to allow the top to "float" just a hair.
Adding a thick skirt won't be as necessary or have as dramitic an effect because you have already damped the sounds going "down". At that point the "up" reflected sounds are all thats left.
Ideal would be layers of soft,.dense, soft, dense, etc. and all things softly anchored.