airrabbit is quite right. the TWA L1011 in question would have flown just fine...knowing if a system like a shaker or pusher is in action for the wrong reason is part of the pilot's job.
certainly a pilot might have a moment of "what the F..." but a quick look at the airspeed and other instruments would garner a response like: Stick Shaker in error...ignore...get the checklist out.
I had an eroneous shaker on takeoff...ignored it and returned to home base with a normal landing...mx dried out the circuit with a hair dryer and it worked fine.
IF the crew of Colgan 3407 had done NOTHING when the pusher pushed...absolutely nothing...more people would have survived a crash in an unstalled airplane than what did happen.
A good pilot is constantly (and on a subconscious level) analyzing many many things during a landing approach (see Davies book) watching out for a stall should be high on the list...