Gamefly has millions of members so yeah it might take a while but if you got the e-mail saying they shipped it on 6/30 and its the 9th (as of when i am answering.) then thats over a week. Gamefly would normally send an e-mail survey asking when you got the game so thats where you can tell them. Hope this helps.
Its actually not possible to put an add-on in a disc and play it anywhere. You're going to have to buy it. But i suggest to buy Skyrim and not rent it. Renting it just ruins the experience. Because you would not want to give it back. Also Gamefly doesn't answer these questions we do.