It's rare for the Beast not to make an appearance but it can happen. No character is guaranteed at any character meal.
The Beast is usually there for all the dinner period. He meets for approximately 30 minutes at a time and then takes a 15 minute break. He doesn't visit the tables. When he returns from his break, he is announced and walks through the dining area, waving at his guests before he goes to his meeting area. You can only meet the Beast when you was finished dining and have paid your bill. You will be asked when you line up if you have finished dining. You cannot return to your table once you line up to meet him. Sometimes the line gets long, however we have never waited longer then 15 minutes. Usually it's closer to 5-10. It's one of my favourite meet and greets.