No, of course banning abortion alone would not be sufficient. Stopping underage sex simply requires that parents know what their children are doing and where they are going, and forbidding them from going places or doing things where they might end up "getting laid." No going out to unsupervised house parties where a bunch of minors are getting blackout drunk and the like.
Of course, some kids can and will lie to get around this, which is why I keep repeating over and over that the culture in a broad sense instills the belief that underage sex is Not That Bad, creating a self-fulfilling prophecy. As a parent trying your best in an otherwise degenerate society, yeah, it's gonna be hard to guarantee that your kid isn't able to slip something by you somehow. But the stronger the community is and the more united they are in a belief that teenagers should not be sexually active, the less of a possibility this becomes. The Amish, for instance, do not have rampant casual teenage sex as the norm in their society.
Teenagers should not be taught how to have sex. If we agree with the premise that teenagers should not be having sex, it is incoherent to then teach them how to do it anyways. To say that this sends a mixed message would be putting it mildly. Those who do have sex anyways should be met with harsh social sanctions, and if a child is produced, expected to marry. Again, this is the Amish approach, and it is the correct one.
