If there is a particular place you want to eat, then the answer is YES. If you just want to be able to eat somewhere, if any old place will do, then the answer is no. You'll be able to call Dining the day of and get an ADR for many places, so you won't go hungry. Plus, there's always counter service. You won't be able to call the day of and make an ADR for LeCellier, Chefs, Whispering Canyon Cafe, Ohana, Cindy's Royal Table, Cali Grill, 1900 Park Fare, Chef Mickey's, etc.
I will also say that even if you don't want to make ADRs before you arrive in WDW, you should call and make an ADR before you show up to a restaurant. There will be lots of things available the day of. Not the most popular dining locations, but something will be available. If you just show up and hope for the best, you may be disappointed.
I never understand why people don't just go ahead and make ADRs just to have a back-up if nothing else. Then if you don't feel like going to the restaurant, cancel the ADR. At least you'll have an option....
Edited to add: 2009 will be our third year straight going to WDW in January. We always make some ADRs. Some of them we keep, some inevitably get cancelled. We routinely call Dining on at least one or two days of our stay to see what's available. We've gotten Artist Point, San Angel Inn and Rose and Crown by calling the day of. You will not go hungry, but your dining options will be limited.