Is it a tumbler or a vibratory cleaner?
Some of the vibratory media (corncob or walnut shell) can get stuck in the flash hole or even block the primer pocket. You'll need to check this before priming.
If you de-prime after cleaning then you'll remove any stuck media at the same time but the pockets won't get a cleaning (though they don't need it much and they won't get very clean with this method anyway).

If you're wet tumbling with steel media I doubt you'll get many pins stuck but I have had one or two occasions where two pins have managed to stick in a small flash hole.