Additional carpet in double stud wall cavity? why not?

Hi all, I am considering attaching a layer of carpet to the internal timber frame of my double stud wall cavity…. I am doing this in an experimental attempt to improve sound proofing/ insulation. (and I have a shit load of carpet lying around). Please take a look at the attached image to understand exactly what I mean. Are there any reasons not to do this? Is the carpet dense enough to be considered a third/ fourth leaf? Thanks very much for your advice as always.

P.S The Carpet will also assist in Holding the insulation in place. bonus

Daryl, No it will not create an extra leaf. But it's pointless either way to add carpet anywhere... It has no isolation value, little absorption value, it's mostly not fire proof. Thrash it.