That seems to depend on the retailer. If it was purchased at somewhere such as the Apple Store, Best Buy, or Future Shop it does indeed seem to register the date of purchase through the point of sale system. For smaller authorized resellers the computer becomes registered to the owner during the initial set-up process.you don't need a receipt to register it. Once the computer is scanned at POS, it will become "live".
That being said, it is always a good idea to hang on to the receipt in case it's ever required. For example, if you purchased a computer at a small authorized reseller you may notice after registering it that the purchase date is a month or two off (which is when the authorized reseller ordered the computer from Apple, not the date in which you purchased it). To update your date of purchase with Apple, you typically need to fax or e-mail a scanned copy of the receipt.
I wouldn't worry about it too much though, as the above example is the only case I have ever seen the receipt required.