Dear Pax2908:
On any complex aeroplane, AoA data is primarily used for stall protection, A320 not being an exception.
As for stall warning in normal law methinks that FCOM is referring to spurious warning triggered by damaged AoA vane. IIRC Vsw (altn and direct laws) is near Valpha prot (normal law) and it's a bit greater than Valpha max and stall warning really should be inhibited in normal law - otherwise one would get continuous warning during hard WS and GPWS escape maneuvers.