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.
What about condoms? They don't do anything but stop the sperm, and they're important in preventing STDs, not just for gay people but straight people as well. Should they be free in states that ban abortions?