Personally, I'd just shoot it unless it's really crappy looking. And I'm talking so bad, no amount cleaning is going to help it enough.
About tumbling effects:
I've heard a similar story from two veterans who didn't know each other, although both were in artillery. While not exactly about tumbling, I think it applies.
Each story is similar: In the M-14 days, their crew was given a 20-rd box of M80 ball (.308), and this box rode in the cab of the deuce and a half which towed the big gun. After untold months of this, someone had to fire their M-14 for a qual or something and grabbed that box of ammo. The first shot, or one of the first shots, locked up the gun.
I only remember one of these two guys saying they pulled down the ammo for a look.
The one who did said they found the powder in some rounds varied from the original extruded (stick) shape, presumably due to the vibration of riding in a metal truck cab. Some looked OK, some looked like the kernels were snapped in two, others were really crushed, and many had a mix. This could have altered the burn rate of the powder, and by a lot I would think.
I would think tumbling could cause a similar situation with extruded powders, although it might take a longer time than I would tumble anything. I don't think you would get the same effect with flake or ball powders.
I know there is a lot of probably/assume/could have/maybe in those observations, but while I have briefly tumbled small amounts of loaded ammo in the past, I haven't since hearing this.