Been there - tried that - didn't work very well. I take all my moon clips and place them in a can and let them soak in solvent for 24 hours and then wipe them off with a rig. If would be very convenient to be able to just toss them in a machine but doing them by hand is the only way I have found to really get them de-funked. Using a tumbler on dirty clips will also trash your media and make a mess of the bowl which you will then get to clean out with solvent and a rag. No free ride I'm afraid. I have also heard guys claim they use their dishwasher for this job.
You can't make this stuff up.