I've been a little late for some ADR's without repercussions - obviously you don't actually get in the "line" for next available table until after you check in. I would imagine, though, if you are significantly late, you might risk losing that reservation and a table not being available.
We were about a half an hour late for breakfast at the Kona Cafe (taxi didn't show up) and the CM said they were just getting ready to give our spot away.