Yes, prospective parents have the right to take the baby for a medical check-up to a pediatrician of their choice so that they are completely satisfied with the well-being of the child. However, the baby is usually accompanied by a representative of the agency. If the prospective parents desire any specific medical procedures to be conducted, they can be performed only after the approval of the agency.
One must keep in mind that every agency has its own panel of doctors that conduct a thorough examination of each child available for adoption. The complete medical status of the child is recorded and the agency is duty bound to disclose all the known medical facts about the child. If the family medical history is available, even that is made known to the parents during the identification process.