Will I be able to carry my baby to term if I my placenta has shifted to cover my cervix?

No. When the placenta covers the cervix, the condition is called placenta previa. Ultrasound can usually detect it. In many cases bleeding occurs or delivery is planned before the due date. Ideally delivery would be close to term (within two weeks of the due date). However, often bleeding is heavy or persistent enough that the OB physicians feel it is important to proceed with an abdominal delivery.
Be patient &vigilant. The placental attachment of a complete previa may not provide as much nutritive surface to keep baby at the same percentile as earlier but enough growth to get baby stronger & ready for delivery. Make sure you understand your ob's warning signs & instructions on when to call the service or come in for evaluation. Weekly visits will monitor growth & help decide when to schedule a pre-labor delivery.