Can a pinched nerve go away without treatment?

Yes and most do with: 90% resolving over time especially when caused by a disc herniation. That is why so many different types of practitioners and techniques can claim high success rates as the natural history is also one of high success. Treatment tends to help manage symptoms while you heal and hopefully teach you how to minimize recurrences with lifestyle changes such as exercise, not smoking & staying trim.

Yes: With conservative management, that is to say nsaids, rest and heat therapy the symptoms can be improved. Not all pinched nerves need to operated on.