I have been lucky enough to have my EDD's fall when my OB wasn't having holidays but he didn't make it to the birth of my 4th due to a family commitment and me having a rather fast labour that he couldn't make it to, though he did come in when I had a secondary PPH 2 hours later.

He works with a group that all back eachother up so perhaps you could find out if your OB does something similar and arrange to meet with the other OB before the birth.

I know it's not the thing you want to hear but there is no guarantee that the OB will make it anyway. If it is a particularly busy day or an emergency pops up then you will get someone else because they won't leave someone in theatre