I think it's possible, even likely, that many pilots would deselect the FD's if they observed a blank black airspeed tape on the PFD, not necessarily only in response to a particular ECAM message.
And if they chose not to, they would, as a minimum, disregard any FD commands until things were sorted out and FMA modes were confirmed as those warranting use of the FD.
CJ: Yes. (I've flown those older type aircraft too. They are different.
)
(BTW: V/S is the default restored initialization for the vertical mode, but if you're within capture parameters for the selected altitude, the mode may jump right to ALT* or ALT CRZ*.)