I just got my white 16GB iPhone replace in Grand Rapids, MI last week and all "white box" iPhones (phones that come out of a unmarked white box) are all refurbished. Everything on the outside is new, so it will not have any scratches on it or anything. The batteries are also new. The inside components may or may not have been used before, so some of them could have been used, some of them could be used... I guess whatever they replaced is new...
Sadly, I replaced one problem for another. My phone had some cracks in the case, it had dust under the screen and when you shook it, it made a very loud rattle noise. The genius was surprised and replaced it... But I have a case on mine and didn't realize that the phone has some light leaking from the left side of the glass... and I live 2-3 hours away, so I can't really go back easily...
But yeah, when you go in they'll give you a refurb. Looks new, battery is new.