Yes, you will have a problem. The only acceptable proof of coverage is a declarations page OR an application with a paid receipt. Copy of the check is not acceptable, the argument is that that you have no way of knowing when they gave the check to the insurance company. The insurance co. should be able to provide you with a receipt showing when they received the payment.
To add to GL's post aboce - we do have a fax from the insurance agent, to the lender, of the fax cover page, the application and a copy of the check. Said fax, application and check are date before the loan closed and funded.