That being said, a ten-year birth control device would solve most tennage pregnancy.
You indicate that the program is voluntary. It would only (more or less) solve the problem of teenage pregnancy if there were enough volunteers, and it isn't at all clear that there would be.
We can hope for lofty "bring back religion to schools" but realistically, that will never happen.
A religious approach would likely emphasize abstinence only sex education, a failed policy. So it seems it wouldn't help the situation overmuch, putting aside the fact that it will never happen anyway.
So all I look at it realistic solutions
Most Americans are still horrified of killing human embryos at a phase when they are a pathetically small collection of cells with zero neural activity -- preferring to treat them as if they are like you and me -- yet you think it's realistic to start locking children into binding agreements that require the government to surgically install devices into their genitalia in order to control their reproductive habits? OK.
People love money.
So why not just give them money, then? Most of the kids won't end up in college anyway ('most' in the logical sense of 50+1% or more).
Several countries have 'conditional cash transfer' (CCT) programs which initiate cash deposits to poor persons based on their behavior. I don't know much about them, but I read good things about their efficacy. Rather than usher in some dystopian future of forced surgical procedures, a CCT program is a non-invasive solution that would incentivize behaviors that tend to minimize teenage pregnancy (continued educational attainment, attending a sex ed class, etc.) with cash to the mother's account(s). If you link such a program with welfare benefits more generally, there'd be even more incentive for even more people to act in a way conducive to solving the problem.