Notwithstanding any other provisions of the code to the contrary, the county board shall not be required to submit its budget for approval by the state board of education as provided by section twelve-a, article eight, chapter eleven of this code and sections six and seven of article nine-b, chapter eighteen of this code, until the tenth day next following the state board's transmittal of final state aid computations following the adoption of the state budget, but no later than the thirtieth day of May: Provided, That, in any year in which the state budget is not adopted on or before the first day of May, the state board may require the county board to adopt a preliminary budget and to submit it to the state board no later than the thirtieth day of May, and when final computations of state aid are transmitted to the county board, the county board shall make such adjustments as are necessary prior to final adoption of the budget.