I found your question interesting so I grabbed some handfuls of my dirty copper jackets and ran them through my inexpensive HF rock-tumbler with hot water, Dawn and a little Lemi-Shine (no steel pins - I don't need that headache) for a half-hour, just as if I was cleaning my brass cases:
Before:
After:
I'm not sure if the juice is worth the squeeze but I did find that it was now easier to spot any lead, rocks, etc.