You're right. Theplane will stall once it AoA was exceed.
But for the aircraft at cruise, in order to maintain the level altitude you need a
constant lift to counteract the weight.
So, if the pitot tube is frozen and send the data to the autopilot and
auto throttle that the airspeed was way to much higher the autothrottle will
decrease the throttle which slow your airplane down. Normally, when the aircraft
slowdown it want to go down. However since autopilot want to maintain the
altitude that pilot dial in or FMC, the autopilot will pull the nose up which increase
AOA. So the aircraft will continue to slow down and pitch up untill it stall and
then crash.
This is how I think it was work. However, may be the ice might form on the wing
and make the aircraft stall faster too.
Best regard