Does pepper go bad? I’m wondering about storing unground pepper in this grinder?
You mean coarser grains?
For powder (I powderize sea salt sometimes), I use a blender… It makes regular sugar into powdered sugar as well.
Still haven’t found a good sea salt mill (sometimes large chunks do get through), but I’m not spending $30…
WAAAAAY over my head! 
Obviously ground pepper loses its flavor much more rapidly than peppercorns. But peppercorns don’t last indefinitely. To get maximum life, keep them away from moisture and light. Storing them in a mill does keep them out of the light, but won’t keep out the moisture like a sealed container. So if you aren’t planning to use the pepper soon, you can do better than a mill for long-term storage.