I often place loaded pistol ammo in my tumbler to remove case lube. It is in there about 15 to 20 minutes. I haven't found any problems with my ammo from doing this. Sorry I can't help you with rifle ammo since I have never tried it.
If you want to keep it looking good longer try adding some NuFinish polish to the media. When doing this put it in the media and let it run at least 15 minutes without any cases. This gets it mixed with the media pretty well. Then add the cases you are cleaning. Check it every 30 minutes and stop when you see the results you are looking for.
The NuFinish will leave a very thin amount of polymer type sealant on the cases keeping them from tarishing for quite a long time. I have not seen any negative effects using this method.