If these sensors have a common failure mode (eg. always showing lowest possible value after blowing up), this could be bad. If they just produce junk, it's unlikely they would agree, and MCAS would be turned off.
In addition you should be able to cross-correlate with gyro and airspeed sensor, not to check the absolute AoA, but certainly determine if delta-AoA is near zero (frozen) or not.
But the readings with the vane flapping around should have a significantly higher variance than the readings where the vane has frozen stuck. In addition, a sliding average should show the mean moving around significantly compared to the frozen readings. Surely they should be able to discriminate between these cases based on those factors, especially when cross-correlated with other sensors.
For example, if the AoA sensors say the nose is too high and the flight control software trims down to compensate and then it doesn't see the AoA sensors report lower pitch, couldn't it check the Attitude Indicator (AI)?
Angle of attack and attitude aren't necessarily the same, because the wind vector is not necessarily parallel to the ground, but AoA changes and AI changes should be well correlated most of the time. If trim changes are showing up in the AI data but not the AoA data, then you've probably got malfunctioning AoA sensors.
My understanding is that with still air, AOA is basically the difference between the attitude and the vertical direction of travel. (i.e. in still air you are climbing at an angle of 5 degrees with the nose pointed up at 10 degrees, your AOA would be 5).
So in my possibly flawed understanding the better way to approximate real angle of attack when the wind is parallel to the ground would probably be to take airspeed and rate of climb data, perform trig to get the angle of climb or descent as seen from the air reference frame (cf. airspeed vs groundspeed). Then subtract that from the gyro indicated attitude, and you get an angle of attack approximation that assumes no up or downdrafts.
That combination might yield something better to compare against the AOA sensors than just the attitude value. (Although I would agree that if it changing the trim causes the attitude to change but not the AOA sensor output, something is probably wrong.)