Magento: Enable the adding of products to cart that's invisible to the customer.

Problem: On or site, certain products that are ordered are shipped out with extras such as a promotional flyer or a certificate. We wish to keep track of these extras in inventory by setting them up as simple products and having them added to the order placed by customer. However this needs to be invisible to the customer. Solution needed: A product should have a "Add additional product to cart when ordered" functionality. So for example, when ordering product x, product y is automatically added to the cart BUT this is totally invisible to the customer, s/he won't see it in the cart, (including the cart drop-down), checkout, transactional emails sent to customer or the in the orders in the My account section. It should be seen in the email sent to the warehouse as well as in the backend and should be shown in all reports run on products.