You will likely still be able to get many ADR's but perhaps not the most popular places- like Chef Mickey's, Crystal Palace and Le Cellier.
Places we've enjoyed as walk-up diners include Akershus for the Princess dinner (they couldn't get us in for about 90 minutes, but they told us that when we walked up and they just put us down like a reservation...technically perhaps this is not a walk up, but a same evening reservation made at the podium...the same evening The Garden Grill offered us the same), Nine Dragons (perfectly good Chinese food), The Plaza (at the MK, mostly sandwiches and ice cream, but good!), Olivia's at OKW, Hollywood and Vine, 50's Primetime, Mama Melrose, Boatwright's at POR....and I'm sure others I'm not remembering. Some of these places have become favorites after trying them on the fly.
Be flexible and definitely call to try to get what you want....but if you're stuck without an ADR (or your plans change) be flexible and just ask!
Suggestions for that date night, if you can get reservations (just try!) - Artist Point at the WL, Jiko at AKL (best meal ever when we ate there, though the chef has changed now), California Grill at the CR, Kona Cafe at the Polynesian.