I would say with how popular the DDP and ADR's have become, it's a 99.9% chance you would need an ADR. Obviously you can always try going without an ADR, however I would suggest making one since Chef Mickey's is very popular. Now a few years ago my family and I went there for dinner without an ADR after being told non were available, however we still got in after waiting about 45 minutes as walk-in's which was not that bad. Plus since we were staying at the Contemporary we did not mind the wait, so it's not like we were rushing to be somewhere else.
I think you'll be seated eventually. When we were there in September during free dining they were accepting walk ups. They gave them a beeper thing and had them wait. That was during breakfast though.