My iPod's battery was out of charges, so I followed the steps to mailing it to Apple so they can repair it and I went to a UPS Store near me and gave it to them, so they can send it, like it says in the instructions from Apple. I forgot to give them the paper that i printed out. Will Apple know that the iPod is in need of repair or will they think that some random person just sent them an iPod? I did the online form thing, so I know they know an iPod is being sent to them, but I don't think they know that the one I sent is the one they're expecting.
Why don't you contact Apple and ask? We're all just regular users like yourself here, and have no idea what Apple will think if they receive an unlabeled iPod.
While you probably should call Apple to check, remember that your iPod had a serial number. If they get a strange iPod in the mail, they should be able to link it to your online repair order, where you entered the serial number (right?).
Well, I called Apple and it turns out, UPS sent ti to the main office of Apple in Cupertino, so all they had to do was get it from the main office and bring it to the repair center. It's going to take 1-2 weeks, but I can wait.