I know someone who is in the same boat as your son. He has been in an intensive 18 month inpatient rehab program and another intensive outpatient program and he STILL uses. I think it'll depend on the person, timing of going to rehab and the treatment program. He still uses and is probably worse off now then before rehab. I hope your son gets the help he needs.
I understand the shame in not telling your family about his addiction. I didn't tell my family about my boyfriend's alcoholism until just recently. While their reaction is like any reaction (great concern for both me and him), they still accept him for who he is and still like him just the same. I feel as though keeping his addiction a secret is a form of enabling and I don't think you want to enable anymore than you already are. How he reacts to his family knowing his problems is HIS problem, not yours. I understand you're concerned it'll make him want to use more but as another poster said he'll use when the sun shines and when it doesn't. It'll just be another excuse to get high, at that point.
Hope things go well for you and your son!