Ok, this has to be cleared up. Yes, you can download songs for Rock Band on your friends console (or anything from the marketplace for that matter) and use it on your Xbox, but it will have to be redownloaded to your 360 before it can be played, every time. This means if you buy it from your friends 360, you redownload it on yours, you can play it, but as soon as you turn off your 360, the content will be lost. You will have to redownload every time you want to play it, and if you are banned from Xbox live, you will not be able to do this. Buy the Rock Band songs from your 360, I don't know for sure, but if you get banned, chances are you will still be able to play the songs. Also, I recommend upgrading to iXtreme 1.4
-edit- I just re-read your post, and I don't know if it goes for the same with switching hard drives, but this method I said above is for just recovering your gamertag on your friends xbox.