The Metro that I fly has a stick pusher yet it's all cable flight controls. The stick pusher works with a system called SAS (Stall Avoidance System). The SAS is a computer that will compute your V/Vs (kind of ur AOA), and activate when u reach the 1.1 V/Vs range. A servo will push the control collum foward, u can overide the pusher if u apply over 60 lbs of force with your arms. The SAS uses various elements as inputs, such as your AOA via a vane on the nose, your flap position, and ram air measured at the co-pilot's pitot.
The SAS triggers a horn +10 to +5 kts from stall, and the pusher from stall +4 to -1. It deactivates itself at 140+ kts.
As far as the heated pitot system, I have never seen one with ice on it while heated. On my plane, I have 2 independants pitots, one for the co-pilot, one for the pilot.
If one of the input of the SAS gets wacked, the SAS will provide false information, maybe activate the pusher. We do have the option of shutting the SAS off, with the inflight limitation of "Do not stall aircraft with SAS inop".
That's my lil turboprop, others probably have different systems.