If you ran that snake down the barrel 30 times it still would not be a true DEEP CLEANING. While they have a lot of surface area to "patch" the barrel, they have a tendancy to get dirty and all you're going to do is re-deposit crud back on the bore by using it. Luckilly you can wash them so if you only use it say between shots, you should be ok. You need to get a bore cleaner/powder/fouling remover in the barrel and let it soak. Then you want to use a brush to physically remove the gunk lifted up by the bore cleaner and then dry patch until the patches come out white. When I Super Clean my guns, I do this process twice, and even though my barrels are all highly pollished, I still get a little bit out on the second go around. If I'm shooting right after cleaning, I dry patch all the oil out of the barrel and then even run an alcohol or card and choke cleaner soaked through to be sure it's squeaky clean.
Pollishing is a whole other sepparate and different process all together. It involes taking out imperfections in the bore and smoothing the metal ever so minutely every time it's done. Cleaning, especially with just a boresnake is not going to pollish the bore of any shotgun. You still need to Super Clean after you pollish btw. If you are interested in doing either to your gun, I would suggest reading the stickys at the top of the Turkey Gun Forum. They will get you going in the right direction for sure. Good luck!
