Well, first of all you don't get AppleCare, that's a separate product that you must purchase to extend your one year coverage to 3-years. You do get 1-year manufacture warranty from the date of purchase. If you purchase through Apple, the warranty system is automatically updated and your serial number will show up on their support website. If you buy from Amazon, Apple warranty will most likely ask you to submit purchase information to confirm the coverage dates.
There is no downside to buying from Amazon. They often sell them at discounted rates and I know some even save on having to pay taxes. I would still prefer Apple over Amazon, especially if you're using student discount with which you also get a $100 iTunes card + $100 of the 13" MBA.