Yes, it works great---with a few caveats. It blocks high frequency sound very well but it is only partially successful at curbing low frequency (high energy) noise like mechanical noise from an engine. The mat used along with lead sheeting really makes a big difference in dB reduction. The egg crate foam stuff really isn't satisfactory for our industrial type noise. Products like Dynamat work less well than lead for low frequency noise and they are quite expensive. It works because it is basically a dense sheet of bitumen. You can make your own Dynomat by buying a roll of roof valley bitumen at Home depot and applying aluminum foil to one surface and using the other side's sticky surface to hold it in place.
Back to the caveats. Many of the repurposed rubber mats are porous--water and air and sound (to a limited extent) will pass through. The less porous the better. A layer of home made Dynomat on both sides of a porous rubber mat helps a lot.
Add a dB meter app to your phone and do a little study of noise. Try different combinations of materials and see what you like best.
I used 2" of fairly porous rubber mat with an inner and outer layer of home made Dynomat to line all surfaces of the drawer my already quiet Yamaha generator lives in. The result is that a person standing next to the genny drawer has to be told the genny is running before they are aware of it.