Yes. I decap on the Dillon, then **dry tumble* for about 30 minutes to remove the lube, then wet tumble for 2 hours. The brass looks brand new after the wet (stainless) tumble.
I also tumble (wet or dry, doesn't really matter) before the decapping run on the Dillon. I don't know how well or even if the brass would run through the machine without at least a little cleaning after having been fired.
Heck, I even dry tumble my finished ammo for 15-30 minutes. Of course the prepped cases get lubed before the actual reloading and I want to remove the lube before running the ammo through my guns.
It's absolutely not necessary to go to this much trouble, but I generally put an equal value on form AND function.
RE: Dust... I don't seem to get much dust from my walnut media. I was using corn, but no matter how often I changed the dryer sheets, it seemed pretty dusty. I pop a new dryer sheet cut in 1/4's into the media after each ~10 hours of runtime. I also dump in a bit of Nu Finish car polish in at the same time. My ammo is very shiny when I'm done with it!