I always de-prime before tumbling. I like to have the primer pockets clean, before I reload.
The primer pocket and/or flash hole can get a chunk of media caught in it, depending on the size of your media.
I leave the de-primming pin installed in my sizing die, to punch the chunk of media out, just incase I miss one.
I use "birdie litter" crushed walnut shells in a Lyman 1200 Auto Flow tumber.