Lone, if the plane has been showing a ground speed of say 475 kts and an airspeed of 275 kts. The airspeed goes away because somebody insulted the pitot probes. If the ground speed drops but stays above 200 kts should the plane decide it doesn't know AIR speed so it should not impolitely sneer at the pilot about the plane stalling? Seriously, simple loss of airspeed is not a total loss of the ability to make a usable guess of airspeed for at least a few minutes with regards to stall warnings in a sane world.
Unfortunately, in the case at hand, I really don't think that would have made a difference. PF lost his head through lacunae in his training, unrecognized fatigue, or some other factor we can only guess about. PNF was not being communicative enough calling out proper procedure so that the cockpit TEAM were working on the same problem with their full brains. (And don't forget that two day old pizza for waking up the PF.)