What are the chances of the slow speed being due to unreliable airspeed? A blocked pitot will over read in the climb, hence the pilot or autopilot will continue to raise the nose to bring the speed back, before identifying the problem. The over speed comes quickly and the autothrust will bring thrust to idle.
Which aircraft could accelerate on the speed tape with thrust at idle for the climb?
None, hence the unreliable airspeed being identified requires, a autopilot off, autothrust off, flight directors off.
Then set a reliable thrust setting with about 3 degrees nose up, wings level and all will be fine, survival wise.
I never flew A320, but instructed on A330/A340.
On the other hand, if there is a rapid climb before disappearance, this would indicate the blocked pitot, translating into a rapid climb trying to hold the speed back, thus giving a low ground speed read out. Not sure where the ADS picks up the TAS, but if speed is unreliable, surely this read out could be unreliable to.