You definitely need an ADR. We went in May, and every table was full while we were there. It is just a tiny place, so it has limited seating. We went with the intention of eating the Kitchen Sink for lunch, but DD wanted real food. Silly kid.
We decided to do this relatively last minute, so I used one of the dining tracking sites to watch specific times for an ADR (we wanted this on our HS day at lunch, and we wanted it as early as possible because we had dinner ADRs). We weren't able to find one until 2 days before, when someone finally cancelled; later in the day, an even better time slot for our schedule came open, and I was able to move to that one.