I don't think JimBob & Michelle would have shunned (or would now shun) any child who went off the rails. They've allowed their children to be around Amy all her life and presumably around JimBob's sister who was living in sin with Amy's father for a long time. I think most of them, especially from Joseph down, would have an extremely hard time surviving because of their piss-poor education and lack of awareness of how the real world works.
However, without the show, I think Josh would have been allowed to go to either Clown College or maybe even Liberty, gotten caught naked in someone's bed and expelled, then bolted instead of going to Jesus Jail. Josiah would have bailed at 18 and found some family who appreciated him to live with and help him get things figured out. JD, Jana, Jessa, and Jinger would have all married and eventually slowly migrated to a more mainstream Christian church and given up Gothardism. Jill would have married a man just like dad and been as unhappy with him as she is with Derick. And Joy probably would have married Austin.
I think after Josh and Josiah, Michelle and Jim-Bob would have gotten stricter, more confining, and more controlling of the younger kids to keep them in line. The show has given them enough money to go on childless vacations and having so many older kids at home lets them leave without any guilt or responsibility. Without the show, I think they would have ended up doing a lot more parenting once the older girls began marrying.