If the expenses are reimbursed under a non-accountable plan, where you do not have to submit receipts and prove your expenses, then yes.

If the expenses are reimbursed under an accountable plan, where the board member must submit receipts and prove actual business expenses and are only reimbursed for approved expenses, then no.  Such reimbursements are not taxable income. (A per diem can fall under an accountable plan as long as the member is required to submit receipts in a timely manner and is required to repay any per diem in excess of actual expenses.)