Media contamination in the open tips will affect accuracy somewhat, especially at longer ranges, but it is even noticeable at distances as short as 50 meters.  It is difficult to measure with even benchrest testing, but it is very evident with lab testing using true test barrels. (barrel mounted in a fixture, no human contact to mess it up!)

I know of one recent case where test groups shrank by over 1/2 moa by not tumbling loaded ammo after it came off a commercial loading line.  The test was done by pulling two samples from the same run. One got tumbled, the other manually cleaned. Series of groups we shot through the same test barrel and the results compared.

That projectile has been redesigned with a smaller opening to minimize the effects of media tumbling.

I tumble all of my handloads, but I always use larger media (bulk "hamster cage" corncob) and never have a problem.  The finely ground media that Black Hills uses is excellent for cleaning the actual cases, but not so great for tumbling loaded media.  BTW, the stuff on mine appears to be walnut as opposed to corncob.

I load all my ammo on stripper clips, so I take the time to remove the media from the bullet tips as I go.

-Troy

I would advise against tumbling OLD ammo, because the powder certainly may have broken down over decades, and doing so could change the burn rate.  But for freshly loaded ammo, especially loaded with ball powder, tumbling won't hurt it at all, and not only gets rid of the case lube but polishes the anealing marks on the brass, if present.  Note that ALL commercial ammo is tumbled clean before being packaged.

-Troy