With spent primers? Nothing will happen, other than a nice shiny new looking casing. I routinely tumble my brass prior to reloading.
I have not researched whether anything has actually happened or not, but the risk manager in me (I have to prepare these assessments all the time as part of my work) would argue it may not be safe. As to the comment that the major manufacturers do it all the time. I have not seen their operations, so I would not know this fact for certain, but again, in undertaking a very simple risk analysis they require workers to use protective eye ware and gloves, etc., for the most mundane of duties. They mass produce ammunition (1000's in an hour). Would they take a risk of having one of those explosive little primers detonate in a tumbler full of live ammo? Not only does that mean a loss of money, but OSHA would be breathing down their necks so fast. Nope, I call BS on that statement and if it is true, I would love to see how they do it.
I know is seeing old video clips of ammunition production during the war, it was all mechanized. Everything polished and shiny BEFORE assembly of the cartridge. I would wager that is accomplished today as well. Hornady polishes first, then puts it all together:
http://www.thetruthaboutguns.com/2012/03/foghorn/how-its-made-hornaday-ammunition-video/
I would not, but others report they do it all the time. Ultimately, it's your choice.