So she's vomiting on the plane (let's hope she hit the air sick bag), and has a fit that left her unconcious. She was probably burning with fever (read sweating) . . . .plenty of fluid to go around in an enclosed environment.
yes that is a problem.
I don't know about the sweating being catagious or not, but it would be a good guess to NOT mess with it.
That plane should NEVER fly again.