I have gotten last minute ADR's, but I don't know that I'd plan to walk up. If you have a smart phone you can check availability on-line and by location.
For example, if it is 4:00 p.m. and you're in Epcot and think you'll stay there for the evening, have dinner and watch the fireworks, you can search for dinner locations in Epcot that have availability that night. You can also check with guest services.
I have gotten day of reservations to Ohana, Cape May, Biergarten and the Wave when we've needed to make a last minute change to our plans. You just never know what you may find with a last minute cancellation.
As a walk-up, you're assured to have to wait until the people with ADR's are seated if you're even seated at all.