From the July Interim BEA report:
"FLAG ON CAPT PFD FD and FLAG ON F/O PFD FD (2 h 10)
Symptoms: Disappearance of the Flight Director on the PFDs, Captain and
First Officer sides, and display of the red FD flag.
Meaning: This message indicates the Flight Director function is selected and
unavailable."
Followed by:
"FLAG ON CAPT PFD FPV and FLAG ON F/O PFD FPV (2 h 11)
Symptoms: Disappearance of the FPV (bird) on the PFDs, Captain and First
Officer sides, and display of the red FPV flag.
Meaning: This message indicates that the FPV function is selected and
unavailable."
We don't really know how ACARS prioritized the transmittal of messages, but they could even have been virtually coincident.
Even if you could use this method during routine flight to determine AOA, it wasn't available to AF447 when the going got interesting.
Machinbird