"In that case, I wonder how accurate the stick shaker would be with taped over static ports ?"
It rather depends on the design of the system.
If the shaker is altitude compensated, then loss of accurate altitude info will have an effect.
If Mach compensated there will be another, differing effect, as the Mach will be in error also.
If purely aoa driven in theory there will be no effect
unless
the sps relies on adc info to 'go live' - some systems are disabled at low speeds, as the aoa vanes are unreliable at low q. In that case the failed/affected adc may cause the spc to also fail in sympathy.
I don't know the specifics of the Boeing system.