Such would not be the case of the airplane in question. It's a very low time/low cycle airplane delivered in 2005.
I cannot imagine it being delivered without systems as I described. New off the line Embraers and even my 10 year old airplane have such systems in place. The data of all systems will be compared and if they exceed the tolerances you will receive a miscompare. Your options then become to switch to the good system, typically regaining control of the autopilot when doing so or if for some reason both main systems dropped offline at the same time (not even a 1x10^9 chance for that) you'll have standby instruments running on their own independent air sources which on a 330 are located left center of the instrument panel adjacent to the captain side PFD.
Even if a complete ADC failure were to occur where you flew through a giant film of jello clogging all of the air data probes the airplane wouldn't fall out of the sky. This would be losing ADC/ADS 1, ADC/ADS 2 and the Standby instruments (note: This doesn't happen) resulting in no airspeed/altitude indications. During cruise time the loss of airspeed and altitude indication would provide little more than an annoyance to a crew. Your navigation systems are still operating and prudence would dictate offsetting course as you will not know your exact altitude. You'll still have attitude control, control of the engines and surfaces and lots of time to find your way to good weather to make a landing in visual conditions. This would be greatly aided with an AoA (Angle of Attack) indication which are options (not standard) on Boeings and I would expect not standard on Airbus given their levels of electronic integration.