No. If your order goes through, you'll see an acknowledgement page and you'll receive e-mail messages detailing your order. If you don't see those messages and don't get any e-mail, then your order did not go through and your credit cart was not charged.
In very rare instances, clicking on the "Review Order" button from the checkout page will send you back to the cart page. This appears to be due to a temporary communications glitch with our payment processor. Just wait a few minutes and try again. You should then be able to place your order.