Yes, it should help to remove the rust. Apply a good coat of it, let it sit for a few hours to a day, and then wipe down. Do the entire barrel to make sure it comes out even. This won't remove the pitting, but Break Free CLP should easily remove the light surface rust you are describing.
Two other products that might help. Kroil oil, a penetrating oil will also remove rust and is typically my "nuclear option" when it comes to this stuff (i.e. fixing an adjustable wrench left out in the rain for years). The other is a cloth that Hoppe's puts out, specifically for your problem. Check the "Uncle Mike" website for it's exact name. But this cloth took the rust off of a Buck pocket knife that I let go through the wash. BF CLP wouldn't get the rust off, but it would. However, it is stronger than you think, so be careful.
Hope this helps.
Matt