Yes, it makes a huge difference.
Once I had completed the install, my naked interior with just my driver's seat was just as quiet as when I had the full interior installed. When I finally put the carpet, passenger seats, door panels, and rear panels in, it was incredible... I would say about 75% reduction in noise.
I did go further than the matting, though. I lined the interior of the front and rear panels with a foam backing that helped immensely (also, this strengthened the front inserts... no weight gain and solid as a rock) I also chose to seal the front doors and rear panels using extra fatmat. It was a bit extreme... but it worked very well.
Also, I am running a Greddy header and AEM shortram- With everything installed I can still hear the engine and my intake, but it is very muted. Obviously this won't cancel out your catbacks, but it will take it down quite a bit (If anyone wants to send me a matching Greddy exhaust so I can test the sound out please do tyty)
And of course your system won't have to waste power overcoming the shake, rattle, and roll. I haven't bought a new system yet, but I tossed in my old one to see the difference- running just an old Alpine deck, two front stock speakers- original oem from 1995, and two rear JBL, the system blew me away. Friends thought that I had installed a sub when I showed it off... but then again my friends are idiots.
Can't find my final install pics, but here are some early layers...
I tried everything on my install...
I found Fatmat and the stuff from Elemental designs was just as good as any of the expensive name brands in terms of sound control and adhesion. Prices on name brand are just too much.
Fatmat screwed me- I ordered on the website and they never responded, so I used an eBay dealer. One came through, but then when I ordered more he was unable to fulfill the order. At the time I guess Fatmat was having problems getting inventory shipped to everyone, even dealers. (I say they screwed me because months after cancelling my order they shipped my order... one reason I layered so much- I was too lazy to send back)
www.fatmat.com
Elemental Designs... I love these guys. They have just as good of stuff as anyone, but they offer it by the foot... Also they have that neoprene stuff (buy a roll of insulation tape... same stuff) The closed cell stuff has no weight but closes out all sound- but you have to cover every single inch otherwise it wont work.
http://www.edesignaudio.com/edv2/index.php?cPath=24
Lowes/Walmart/Home Depot: Foam tape. You can get in variable widths, thickness, but I always use the big rolls that are 2" in width. This stuff is great to cheaply control sound and vibration. Cost is about 6 for a square yard (about what a big roll is) Moisture, heat, and cold proof- just don't stretch it when you install. I used this to deaden my trunk lid (i have an ej1) It did a great job and added no weight.
Good luck on your project!
/btw
//those goofy knee pads they sell are a godsend