No it doesnt have to work. I bought to broken 2nd gen nanos on ebay over the summer for a penny each with free shipping and I used one to get 10% off my 32gb touch and Ill probably use the other for an iPod Classic. The nanos were missing the bezels and had dents so as long as its an iPod your good.
Apple gives 10% off a new iPod for trading in your old one. However, you can get much more for your iPod on ebay instead of trading it in and put that towards your purchase.