This is actually kind of terrible. A compromised ipad could either compromise the planes actual vital systems for one, any time 2 systems are in communication a compromise is possible, and for two it could introduce a subtle numerical error.
I can't imagine a scenario where this ought to be allowed.
Sort of, at least in general aviation. Some of the newer avionics have bluetooth interface. For instance, popular GTN-series nav/comm can accept flight plans from Garmin Pilot software running on iPad.
Now, the iPad part is not certified, but the nav/comm (including software) is.