Obamacare does not make an exception when it comes to the health of teens and young adults, and all sexually active females for that matter. Obamacare will guarantee that people have adequate access to birth control, a vital part of women's health. So Obamacare will win despite the Republicans attempts.
This hits home because where I live we have a well-known store that is owned by Christians. They do not believe in birth control. They are trying to fight this policy based on religious freedom. So far they have not won. So, I would say that there are currently no exemptions to the birth control requirement.