Can it? Yes, if your bank allows it. But it's increasingly considered not to be a best practice. Since the payee business doesn't bank with the paying bank, the paying bank won't have any documentation on who is authorized to indorse a check on behalf of the business, and present it for payment (via an exchange for a cashier's check).
Most banks have adopted a best practice of telling the payee business it will have to deposit the check in its bank account and let it clear through the check collection system. A check presented in this way at least has the depositary bank's warranty that the payee received credit for the check, and a warranty that the indorsement is genuine and authorized.