Yes it does, next time to make this easier be sure to include the order number along with the model number (e.g. A1278 MB991LL/A, which would be a mid 2009 MBP w/ 2.53 GHz Core 2 Duo). Just putting A1278 can refer to any 13" MBP from 2008-Current.
As far as I know as a replacement part there was no warranty. I could be wrong though so I would check with Apple. I can say that we have had it for over two months now and the adapter is functioning properly and we have not experienced any of the heating issues that others mentioned so we are still satisfied with the purchase.
If you bought your MacBook Pro in Aug of 2013 New or Refurbished, the Apple Care should cover any issues with your 60W Magsafe Power supply. That is best way to replace it. I did not find the Non-Apple replacement to be reliable (only worked one day). Even though the Apple price is unreasonable (exchange $61 if they're nice, replace $79 if they are jerks about it), the official Apple product from the Apple store is the most reliable (by far).
I bought this and it stopped working after a couple months (one year warranty). Seller sent me a link to print out a return shipping label. The label was addressed to CHINA and I was supposed to pay the return shipping fee. NO WAY especially when this item shipped from Las Vegas. The squeaky wheel gets oiled....I contacted Amazon and was credited back the full amount. Seller is in China??? and they maintain a warehouse here in the U.S??? If I had known I would be dealing with an overseas seller, I would not have made this purchase. In the end, I went to the Apple store and paid full price, but with some peace of mind, dealing locally. Hope this helps.