When it was designed yes, but at the time of the AF447 accident there were known issues with the Thales pitot probes - in fact there was a service bulletin in effect and operators communications from Airbus giving guidance on what to do should the fault arise.
If the crew realized, in the very beginning there was a serious AS measurement failure this would help the PF to act "better"? As per BEA he executed "persistent NU..."
As has been stated, it's not like the aircraft is a joy to fly in Normal Law and becomes squirrelly and unpredictable in any other regime - the whole point of the law degradation design is to keep control of the aircraft as transparent to the pilot as possible. The only major thing to bear in mind outside Normal Law operations is that the hard-limiting protections are no longer there, other than that it's largely business as usual.
The important "transparency" is IMHO much better preserved (attained) if you understand why there was a degradation. In this case (by inadequate sensors) easily manageable as PJ2 commented. My point is: An important parameter (AS is so important, the design put 3 elements to measure it) should be reported immediately to the crew. Or i am exaggerating? And the System can take care without "disturbing"
the crew?