No...
Foam is used for treating room acoustics, not for soundproofing. As stated earlier, Soundproofing requires Mass (density) and air tightness.
The question really is building to a certain STC (Sound Transmission Class) (i.e. attenuating the sound transmission by a specific amount.) With normal building materials, you can go all the way from STC-38 (not too good) to about STC-58 (much better), based on the construction method and amounts of materials.
Short of building concrete walls, your best bet is to build staggered studs with resilient channels and two layers of dry wall. This should give you a STC of about 58 with a 9" gap and properly filled with glass fiber.
But, before you build anything, I recommend you get one of F. Alton Everest's books. One that's pretty good is "How to Build a Small Budget Recording Studio from Scratch." It has details on construction and issues that you'll face. More practical than theory.
Really good soundproofing is difficult to acheive without spending a lot. Also, treating the room isn't cheap either. With a small room, you'll have to deal with Room modes and uneven decay rates and other small room problems.
-keith-
