Under the health information act no he can not by law tell them but please have a discussion with your mom about it. Honesty goes a very long way and I'm sure she will support your decision.
Oh yes, now a days, it's hard to get on birth control for contraception reasons, because most insurance companies won't cover birth control for those reasons. I found that if I told the insurance company that I'm on it to regulate my cycle, they will cover it. But to answer your question, you're 17 years old, so you would still be on your parents insurance plan, yes they would find out.
If you use their insurance to pay for it I think they will be able to see the claim from the pharmacy.