The corkscrew approach as Wikipedia describes it is what the military refers to as a “Force Protection” measure to be used when operating in a high threat environment. It is not a published procedure in the traditional sense of the word, but something that is put in place by the theater commander and briefed to aircrews when driven by the current intelligence assessment of the threat level.
It is not intended to be flown as a precision maneuver like an instrument approach would be. It is a dynamic, eyeballs outside the cockpit looking for a missile, combat visual descent. A high rate of speed is maintained until as late as possible in order to make evasive action possible. Not only is it clearly NOT a stabilized approach, it is actually the exact opposite: Done in VFR conditions, the aircraft isn’t configured until just before landing.
Contrast this with the definition of a stabilized IFR approach from FAASafety.Gov below:
Stabilized Approach Concept. A stabilized approach is one in which the pilot establishes and maintains a constant angle glide- path towards a predetermined point on the landing runway. An airplane descending on final approach at a constant rate and airspeed travel in a straight line toward a spot on the ground ahead.
There is a lot of additional information available about stabilized approaches out there for anyone interested so I won’t attempt a further explanation about the intent. By definition, however, a corkscrew approach is not stabilized.
So, back to the original question: “How does a pilot performing a corkscrew approach make this determination?” (whether the approach is stabilized or not…) The answer is that a pilot performing a corkscrew approach isn’t asking himself those kind of questions. The distinction is completely meaningless.
He/she is looking outside for the smoke trail of a stinger rising from the ground, and working to get the plane to a point where they can pull the nose up to break the rate of descent and slow down, slap the gear and flaps down, and make a tight 180 combat turn to a short final to lessen the exposure time when they are dirty and slow. The goal is to get on the ground as safely and expeditiously as possible and minimize any time spent “stabilized” on a long straight-in approach.
Stabilized approaches are what tactical aviators fly stateside when practicing for their annual instrument proficiency check.