My dad and his wife were 35 minutes late to a Coral Reef ADR this past July (took the boat and monorail instead of bus). They had us wait until they arrived and at that time we were all (9 of us) seated almost immediately. It worked out very nicely.
On the other hand, for lunch at Le Cellier last January we were running late and DS and I ran ahead, as our friend has recently had knee surgery and couldn't move as fast. They wouldn't check us in until DH and our friend had stepped past the arches into the garden (similar to Coral Reef), and since we were 15 minutes late, if they didn't make it in time the host planned to turn us away (unlike CR). We weren't impressed, but the snottiness of the host staff was a big part of that.