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NO, the main reason to AVOID tumbling loaded ammo is that tumbling can break down the powder kernels inside the case and/or alter the burn-rate...resulted in significant (dangerous) increase pressure. As long as the brass isn't pitted or badly degraded due to corrosion, just wipe it with Hoppes #9. I hope this helps!
Deeply split opinions on this topic, I've yet to ever see any data for the powder-breaking-down claims and numerous experimentation by members of firearms forums seem to indicate that even extensive time in vibratory tumblers has essentially no effect on ammo. My take, try a small batch and test. There is nothing overtly dangerous about the tumbling process itself. But also, as the other answer says, if there is no damage that goes deeper than surface level you really only need ammo to be clean enough to cycle and chamber reliably which can be achieved in other ways.
Ronald, this is a split topic Sir, even by experienced reloading experts. (As suggested, try tumble cleaning a small batch first and go from there) : http://bulletin.accurateshooter.com/2008/09/why-you-should-not-tumble-clean-loaded-ammo/