Soaringtheskies, go have a go in an Airbus sim (no stick pusher on Airbus), set it to nighttime with moderate/severe turbulence and then unreliable airspeed along with multiple ECAM messages - all at the same time. Given that you know what's coming you should be able to deal with it, however if you don't know it's coming then given those circumstances it certainly wouldn't be an easy job to deal with. People who say "fly the plane" are correct, but flying the plane won't necessarily be a concern if you don't realise there is an issue with it in the first place.
Edited to add: You can stall an Airbus, there have been several cases of people/mother nature doing it. Biggest problem with Airbus is it has lots of lovely protections (I.e. normal law) however whenever anything major goes wrong you lose them! Not a great thing to have happen and in many peoples opinions it is a serious design floor.