I always de-prime the brass as soon as I can after a match, using a Lee Universal De-capper die in a single stage press. It takes only a few minutes to do the 100 cases used in a typical monthly match.
I do this not so much to get the primer pockets clean (not really necessary) but to provide the hole in the bottom of the case for the water from the wet tumbling (or Scarlett's method of pre-soaking). It makes the whole wet tumbling process much less messy and the drying time is shorter.
Now, you may decide to not wet tumble at all, that's your choice, but if you do, I highly recommend de-priming first.