Growler: I think you will find that the fault is "latched" for the rest of the flight.
I experienced a Dual ADR disagree in flight on a A330 in 1995 which was caused by transient icing of one pitot combined with a faulty ADR. The aircraft defaulted to ALT LAW and remained in such even after descent out of icing conditions and return of normal airspeed indications after some minutes.
Of course, as ever, Airbus may have since changed the software. I believe an increased time delay was introduced before "latching".