Every time I tumble brass in walnut or corn cob media, a large percentage of the cases get media stuck in the flash hole. For this reason, I would not tumble primed cases unless they also had a bullet.
The idea that a bullet in a vibratory cleaner could hit a neighbouring primer hard enough to ignite it is laughable.
The Internet is full of people advising everyone not to tumble loaded cartridges because this causes the powder to break down and change burning rate. Even some makers of tumblers advise against it. But evidence that there is even the tiniest shard of truth to this is non-existent, and lots of people claim to do it all the time. I have seen a couple of studies "published" online where people have thrown a bunch of loaded rounds into tumblers, and taken out some samples every few days and shot them. The last rounds were in the tumblers for weeks straight, but showed no signs of pressure changes. I say tumble your loaded rounds to your hearts content.