Any decent speaker system has some acoustical material inside already. It can be cheap polyfill, fiberglass, or more expensive open-cell foam, but no speaker worth it's salt is an empty box. If you arbitrarily stuff cotton or any other material into the enclosure, you will change the sound, but you may not improve it. Some foam lowers the box resonant frequency, but what you're suggesting is unscientific and it's hit-and-miss.
I'm a little confused about your exact speaker, but I can tell you how dapenning material is supposed to be used in an enclosure. Lining the walls of the enclosure with polyfill or quilt batting can help reduce internal reflections which color the midrange and midbass. More fill can add artificial volume to the enclosure, making the speaker see a slightly larger enclosure.
The limit of this artificial volume is about +10%. If you lightly fill the entire enclosure, you'll get approximately 10% more volume that the speaker "sees". Will this make your bass better? If it's a premanufactured product from Peavy, probably not. Peavy likely designed the enclosure to play a certain range of frequencies with a certain power handling and adjusted all of the parameters to make that happen.
If there's absolutely no fill at all, not even on the walls, then lining the walls will probably make the mid bass cleaner, but it won't do much (if anything) for the deep bass response.
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