Bloggs:--
I've had another read of your post.
If all the Pitot tubes iced up evenly together and there was no immediate discrepancy between the 3 ADR's then the Flight controls may well stay in Normal Law and all protections would still work including Stall Warnings. Therefore if the speed is iced up slow you will get incorrect Stall warnings. Hence the warning in the QRH.
If however if there is a discrepancy between the ADR's the Flight controls will revert to Alternate Law and then the stall warning will only be based on AOA directly from the vanes. Hence the warning in the QRH to respect Stall warnings while in Alternate or Direct Law.
THE TRICK FOR THE PILOT IS TO KNOW WHICH LAW YOU ARE IN