Vibratory tumbling and polishing are industrial processes for deburring and cleaning preparation. BUT they are carefully controlled processes using shaped abrasive media, and exposure times.
What you are suggesting can certainly be done, but you may not like the results.
Taking irregular shaped parts, of different sizes, and subjecting them to indescriminate tumbling will likely give you a bunch of randomly dinged-up parts. Critical edges and surfaces like sears, trigger, and hammer notches may be damaged, and you lose a fine trigger pull. Loss or self-dismantling of parts is also likely. Finish loss to one extent or another is almost certain.
Why would you even consider it? Are you that lazy or careless with your weapons?