No. State Government clears its checks through a bank. In order for the bank to process those checks, they must have an 8 digit clearing code compatible with U. S. Federal Reserve Requirements and be denominated in U. S. Dollars. Foreign checks not compliant with the Federal Reserve clearing requirements cannot clear through the bank.
Foreign checks denominated in currencies other than U. S. Dollars are subject to application of exchange rates which convert foreign money to U. S. Dollars. After conversion into U. S. Dollars, an amount less than, or perhaps greater than, the fee is left. The Secretary of State cannot accept less than the fee prescribed, nor is it efficient to refund any excess.