Yes, this is not a new occurrence for Airbus or Boeing.
I've done the unreliable airspeed training in the sim from 10,000' down to landing. There are a few things you need to think about ( obviously !! ) but it's manageable without any Airspeed indicators. Granted it was in a Sim, reasonably good wx and with no risk of dying ( my heart rate was relatively normal in the sim !!) but we did have a lot of bells and whistles going off for a while which proved a headache for the PM. My job wasn't overly difficult, fly the power and attitudes for the config etc.....
Every Pilot in my Airline did this as part of their 6 monthly recurrent training package.