She would probably need a letter in writing from the boyfriends insurance carrier that she would be covered if the policy is still in effect at the time of the birth. mere statement to immigration would be insufficient. Also child's father would have to guarantee to pay any costs not covered by insurance,
What she is trying is illegal, though we did come across such a case by a Bangladeshi woman whogave birth to an infant and was crossing the US border from Detroit to Canada. So this must be trick many have used in the past. Sadly no marks for honesty here. You can fool people and apply for refugee status and you are accepted.