A torque to yield (T2Y) fastener can be used in most any situation, though head bolts seem to be the most prevalent. The reason T2Y fasteners are used is, even with regular bolts, you are trying to get to a certain stretch length of the fastener. You can usually achieve it through a torque value, but a torque value is a general indication of the stretch, not an exact measure of stretch. With T2Y bolts/fasteners, the stretch is measured through the angle added at the end. A T2Y fastener deforms during this process, which is why they should not be reused. The deformation of the fastener actually gives a lot more accurate stretch and load then does a regular fastener.
I think you basically have the concept correct, but maybe have the fine points a bit off (or aren't explaining them correctly). The original torque value is usually to get all bolts to a clamping force which is equal across the entire fixture and the same for each bolt. Once the initial load is set, then the addition of the angle (in your instance, 180° turn) is used to put a stretch on the bolt causing the additional clamping force onto the fixture. The reason for the initial torque sequence is so all fasteners will be starting at the same point. If you tried to apply 180° from where you've hand tightened them, how do you know each will have the same results? You wouldn't.
