Sorry, but I don't feel the A/P should stay engaged with loss of air data unless it reverts to pure "attitude" hold.
The 'bus and my little jet 40 years ago used, and still uses, the "q" for "gains", which limits the rate of control surface movement accordingly. Doze and A33z can add to this explanaiton and correct me. For example, you wouldn't want the THS to move at the same rates when at 300 knots versus 200 knots. In our little jet, imagine yanking on the sidestick at 400 or 500 knots in "direct" mode such as the 'bus has ( we never had a "direct" mode except in pitch when we were in a deep stall and used a special switch to "rock" the thing outta the stall).
However, body rates are still in play, and they are simple rate sensors that do not need air data. Then there's the attitude reference systems, inertial or basic gyros we have had since the 1930's. So the basic control laws of the 'bus are still inplay, including the AoA inputs, which have a reversion implementation we see in the AF447 once the troop kept pulling with the stall horn blaring.
Next, the basic pitch laws are "gee". Ours did not have the pitch attitude correction due to operational requirements, but BFD. The 'bus system was designed for heavies and their mission/flight profiles. It looks very good to this old FBW pioneer, and my only complaint is the plethora of reversion modes. I would have preferred a single mode between "direct" and "normal" instead of what we see. In other words, no big change at all with loss of air data except you use "standby" gains as we did. Ours used 300 knots gear up and 160 or so with gear down, and we still had body rate inputs to help.