Yes. All of the shopping and inventory can be integrated right into the site using many different pre-made solutions. If the item is out of stock, then it disappears from the page. If there are only 2 left, it will error out if the user tries to place more than 2 into the shopping cart. After the person is done shopping and goes to "checkout", then the information is passed from the shopping cart software to paypal who processes all of their info. It then shoots back a response to the shopping cart software after the person has completed payment with a "status" ie.. Order #3423 was payed for using a CC. If the person pays with some method that takes time to clear, then paypal will indicate that, and your site can pole paypal to see when the order has cleared. I believe PayPal can also e-mail all of this info to you as it updates. http://developer.paypal.com has full details on paypal's capabilities. The best part is that you don't have to worry as much about security when using a service like paypal, since all of the CC #s and other sensative info is only traded between your customer and paypal's servers. Paypal knows more about security than you or I ever will. This means all that your site is doing is displaying available items to a user, tracking inventory, and passing your users along to paypal so that you can take their money from them 
Take a look at oscommerce http://www.oscommerce.com/solutions/oscommerce It does everything you could ever want, and then some. It supports several payment solutions:
Accept numerous offline payment processing (cheque, money orders, offline credit care processing, ..)
Accept numerous online payment processing (PayPal, 2CheckOut, Authorize.net, iPayment, ..)
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