checkboard, this is intriguing
If the pitot becomes blocked, the dynamic pressure & static pressure at the time of the blockage remains the same. As the aircraft climbs, the sensed static pressure reduces (with the reducing altitude) so the ADU subtracts a smaller static pressure from the pitot total pressure, and thus comes up with an increasing airspeed. The airspeed altimeter is now working something like an altimeter.
From that, here is how it could play out. (Possible, not probable)
pitot blocked -> assume AP off and pilot flying -> (add trigger like possible turb/updraft that creates alt incr?) -> AS apparent incr -> back stick command -> alt incr -> AS apparent increase -> backstick command -> alt incr -> AS apparent incr -> backstick command -> rinse and repeat for x interations -> pilot's cross check on alt and / or att indicators alerts him "whoa, I'm climbing" -> PF reaction seen in change 7000 fpm climb to 700 fpm climb (or was that due to power redux???) -> pilot probably slightly behind aircraft at this point -> stall warning or stall indication-> then loss of stall warning -> AS unreliable for X amount of time -> AS comes back -> stall warning returns -> pilot now likely on back up inst scan or partial panel scan on his own display ...
How often did anyone practice this one in the sim?
Not sure how well that picture conforms to reality, perhaps not at all. When a pilot gets behind acft, tends not to say much until back with or ahead of aircraft ... though I've heard a few talk themselves back into a scan on hot mic ...