This is something that I was actually intending to do. I guess I will try something else, maybe just dish soap.
I like the idea of cleaning the dirt off my cases with soap and water prior to putting the cases in the tumbler. This saves a lot of wear and tear on the media. That way, I am using my tumbler to polish the cases rather than to clean the cases.
As a side note, for years I used a tumbling media put out by Lyman that contains some kind of polishing rouge. It would leave a reddish dust behind on the cases. It shined the heck out of my cases, but left this dust behind. Sometimes you couldn't really see it, but in handing the cases, in came off on your hands. As the media became old, more dust was produced. I started to worry that this dust might be abrasive to my dies and my guns. However, the icing on the cake occured when I read the book, "Handloading for Competition". It showed a rifle barrel that was cut in half lengthwise and you could see, with the naked eye, how this reddish rouge was actually impregnated into the steel of the barrel. Long story short, I started washing my cases in soap and water (using a brush to clean the case necks) after tumbling in this media. When I ran out of the media I bought straight corn cob media from then on. In that process I was doing the opposite of what I am doing now: I was using the tumbler to clean the cases and then I was cleaning them again with soap and water to get rid of the dust from tumbling.