I reloaded for almost two decades without owning a tumbler. I cleaned my brass by dropping them in a milk jug with soap and water, shaking them for several minutes, then putting them in the sun to dry. Worked okay, the brass was clean, if not polished.
Nowadays I simply drop them in the tumbler after decapping (there is more than one school of thought on this), but I use walnut blast media and I've never found it to clog flash holes or clog .223 brass. And, it seems to clean the primer pockets. It's a lot easier than waiting for the brass to dry. I don't use polish, I simply want my brass clean.
However, when I'm shooting black powder cartridges, I still take a milk jug to the range with me. A little water, a little Dawn liquid, and I drop the fouled brass into the jug after firing. It seems to dissolve the BP fouling.