Yes you can! The placenta does not act as a storage facility. It acts as a filter. The placenta tries to protect the baby's exposure to substances, but the substances that the placenta deems unsuitable for the baby don't just get stuck and stay in the placenta. The placenta sends them back into the mother's circulation to be eliminated by the body's natural channels.
The one thing the placenta may store is heavy metals. This means a woman who choose to smoke during her pregnancy will have rendered her placenta unsuitable for consumption.
But medications taken during pregnancy should not have an effect.