Any county or school district shall be eligible for State aid for a school psychologist employed for each five thousand pupils enrolled; provided, that each county shall be eligible for State aid for at least one school psychologist. Provided, further, that any district or county may combine with any other school district or county in order to meet the minimum enrollment requirement and for the purpose of securing the services of a school psychologist. When school districts or counties are acting jointly in this respect, State aid shall be paid to the operating units in proportion to the enrollment in these units; provided, further, payments of State aid under the provisions of this article shall have no bearing on the amount of State aid for which a school may otherwise qualify regardless of the fact that pupils with whom the psychologist works may already have been counted for other purposes of State aid.