Hi Charlie,
They really only have to have 19 batters. The guy would have to be the first and last player to bat. Here is some info that I've dugup in my search for an answer. I don't think that it has ever happened. It looks like the most hitters faced in one inning is 20.
"1989 - One Inning, 20 Hitters, 16 Hits
The Cincinnati Reds had one of the biggest innings in baseball history, sendng a record 20 hitters to the plate in the first inning of an 18-2 win over the Houston Astros. They also set records for most hits in an inning with 16, most singles in an inning with 12, and most players to collect two hits in an inning, 7. "
I can't find the box score to see who did what for this game. I'll keep digging.....