I think you meant each transaction, a customer could buy same product twice.
Yes. The payee will have a database full of Bitcoin addresses, preferably derived from a master public key, along with an extra empty column. Each time a person clicks to finish his shopping cart, the database will update that column with the selected products he wants to buy. The buyer will get the specific's row Bitcoin address for funding.
I believe there's a simple way for the merchant's server to verify the transaction's confirmations.
Besides BitPay, do you have any other scripts in mind?