No, because I believe that life begins at fertilization, not implantation. Many popular forms of hormonal contraception can prevent implantation by thinning the lining of the uterus (even if that is not their primary mechanism). Because of that, my view is that popular forms of "contraception" at least have the potential of being unintentional abortifacients. So, not only should many methods not be free, but also many forms of contraception should be illegal.
I really don't think "has the potential of being an unintentional abortifacient" is something that should inform our thinking as to whether or not something should be illegal, otherwise we're in the position of legally prohibiting the consumption of alcohol, tobacco, potentially sushi, etc. etc. etc. during pregnancy (rather than merely frowning upon it as many or most people currently do). I don't think it's reasonable to consider that proportional to the risk of miscarriage, which, sadly, is at least somewhat present in all pregnancies anyway.