Rajesh, mass loaded vinyl is used to sound proof rooms but hanging loosely behind drywall...typically with space between vinyl and drywall.
I'm no scientist, but I question it's effectiveness in this situation. I don't imagine it's a sound detriment, but it does introduce a structural element that I think is worth noting. By covering the box and then attaching the spacers on one has effectively limited the attachment of those spacers to mechanical fastening only, (nails, staples). Leave the MLV out and one can glue and staple the "skeleton" directly to box, a much stronger structural connection.
Seems to me there comes a point of diminishing or nonexistent returns when it comes to cabinet damping. What little this method does to improve damping would appear mitigated by the loss of structural strength. If I felt compelled to use it, I think I'd add strips of it between the skeleton members.
If it interests you here's my take on the sandbox.
http://www.audiocircle.com/index.php?topic=84765.0