Vilas,
I am quite comfortable with our training and QRH. We teach the basics of pitch and power. The BUSS system is there in case there is an ADR, or air data failure and it will supply basic information. Using GPS and other inertial data the system is used to give a simple slow fast display output to keep the aircraft safe while the problem is dealt with.
I have flow both BUSS equipped A/C and non BUSS equipped and the basics are the same. Pitch and power. At altitude it's 3 degrees up and look up the power setting, which at mid weights is about 84%. Because our fleet is mixed we stress the pitch / power method because it always works. If there is a buss display fine but we still go to the charts.
I have never had a problem like this it the Airbuss but I have had an AirData failure on the B737-400. We ended up looking up power settings and using the FMC for support until we descended into warmer air. It was a curious fault, but actually a non event.
All this talk about airspeed and air data is because an Air France pilot and his partner locked the stick full back and rode a stalled airplane into the ocean. This kind of training is and should be done at the primary level. I have flow light aircraft with lost airspeed due to pitot icing. In the region of the great lakes where I trained it was possible to fly in complete clear VFR conditions at 3500ft. and then descend into clouds with light icing and a ceiling of about 1000 ft. It was a great way for a pilot to experience icing and an iced up pitot tube without undue danger.