Yes. The baby(ies) will be under your insurance, not the gestational carrier since she is not the mother. You can purchase an insurance plan for the baby(ies) on their own or you can add them to your current health insurance plan once they are born. The only exception is if you are not a United States citizen. Then, unfortunately you cannot purchase a plan for the baby(ies) and you will have to work out a deal with the hospital for self-pay charges for the delivery.