You can put stones in the pickle but you will want to testy first. Soft stones may react with the pickle causing the surface to lose its polish or become pitted or

. Pickle is an active chemical - that's how it cleans the flux off your metal - this can then react with gemstones. On way to approach this is by
hardness - the Mohs scale of mineral hardnesses. In general, I would expect that anything softer than a 7 Mohs might react with your pickle. Glass is generally 6 so anything softer than glass you will want to pickle a test piece before you use your good stuff this way.
Hope this helps