There's discussion on various new sites, to the effect that the recent crash in Russia was caused by blocked pitot probes. They then invariably bring up AF447 to prove their point that such a blockage will cause an accident.
By itself, these blockages will not cause an aircraft to crash. They can start a confusing chain of events, which, if mishandled will end badly. In the Airbus you'll end up with law reversions...which in themselves are quite harmless....they just convert it from an Airbus to a Boeing.
When learning to fly, all pilots are taught that Power + Attitude = Performance. Airspeed is a performance output...it's a result of setting an attitude and a power. So, even if you don't have a speed reading, setting a known power and attitude will give a known performance result. If I were to lose the air data in a 380 during take off, setting TO/GA and 12.5 nose up, would give a stable climb away from the ground. In the cruise, the aircraft pitch attitude is always 2.5º, and power around 85% N1. If you don't change it from that, nothing much will happen. Descent is zero pitch and idle.
GPS ground speed needs to be corrected for wind to convert it to TAS, but without any thought it provides a rough check of acceleration/deceleration.
On finals, at the target airspeed, pitch is again 2.5º nose up, and power about 23% (thrust). If the speed is correct, that will result in 700 fpm rate of descent. If the RoD is high, then you are slow and need some power to correct (and vice versa). This is the technique used to fly angle of attack approaches.
The upshot is that the aircraft can be flown, without any need to go to any extreme attitudes or control positions. In AF447, full aft stick was being used. Why? In no world will that give you anything other than a deep stall.