I was thinking of an enclosure for my own build. Not to contain dust, but something that would significantly reduce noise. It sounds like that is also your goal. I don't want to drive the people I live with nuts when I use my machine.
I was thinking more along the lines of a tent made of noise absorbing material than a structure with wooden walls.
I'm not sure if acoustic foam and similar products is designed to reduce noise or simply enhance the quality of audio in a home theater for example.
Are you going to line that box you're building with anything?