I think that depends on who you talk to, and how you talk to them, plus the availability of a replacement.
Just before Christmas I ordered a refurb 60GB photo iPod (the older version) that was listed at a good price. I received it two days later. It turned on once, turned off, and never would power up again. I even took it over to the local CompUSA, where I knew someone, and they verified that is was dead.
So, I called Apple Care and spoke with an extremely friendly person, and we had a good chat about it. He agreed that it should be replaced, and I mentioned that I would be willing to pay for an upgrade to the newest video model, unless Apple wanted to do that for sending me a bad one. I got put on hold for about 2 minutes, and he came back on saying that a new model was on the way, and return the old one in the box that it comes in. The next day I had a brand new 60GB video iPod as a free upgrade, and the dead one was on its way back.
So, I recommend having a nice friendly talk with whomever you get in touch with, and give them some options. Good luck, at least they are agreeing to replace what must be a lemon.