I just think secrecy and hiding in these situations reinforces the notion that teenage pregnancy is such a shameful act, an act so embarrassing it cannot be revealed. This is a notion that, in large part, drives young women to want abortions in the first place. It's also a large burden to lay on a young women to shame her for being pregnant, all the while, shame her into keeping the baby.
It also reinforces my opinion that many people in the "pro-life" movement are not "pro-life" but rather "pro-birth." They really could care less about the consequences of pregnancy, birth, or having a child, so long as the child is born.