No: "as at a counter service place where you pay as you get the food. They would be in their rights to refuse to hand over the food and ask you to leave." This

No: "as at a counter service place where you pay as you get the food. They would be in their rights to refuse to hand over the food and ask you to leave." This is exactly the same situation as at Target: you bring a bunch of goods to the cash register. You offer a check. The cashier is going to say "sorry we don't take checks anymore: do you have another way to pay [a Target card, a debit card, a credit card, cash...]. Either you present the alternative method of payment or leave without the goods.