So Goodreader can't work it's usual magic with music files?
You can download and play mp3, and probably a few other, formats in GoodReader. You can't transfer them to the iPod app. Nothing but iTunes can do that. So, nope, no magic there.
You can use other third party music apps, and use Open In in GoodReader to move music files to those (though there are probably better ways). The only one I've used is OPlayer. It is handy for playing some formats the iPod app won't, but it's an otherwise mediocre app.
Now, I said nothing but iTunes can put music on your iPad into the iPod app. That is not strictly true. There are third party computer programs that will do this. I'm not familiar with them, and you need to be careful how you set up iTunes, to avoid conflicts (because you still have to use it for some things). So be sure to do research if you decide to go that route.
Do a few searches for posts by Peled. He operates this way, and has mentioned some programs and setups before.