When I took Hazel to the emergency vet there was one vet, someone like a vet resident, about a zillion vet techs and front office staff. I don't see how one person could do it all.
As for order patients are seen, there's a big sign at the door listing what order patients are seen, starting with life threatening emergencies go first. Since Hazel was bitten by a venomous snake they took her straight back when we got there even though there were people waiting.