C*U only requires pitch trimming for speed changes
DownWindAbeam - I think you have the right idea.
C*U (the variable controlled by the C*U control law) is essentially C* (similar to Airbus) plus a gain times the speed error (current speed - reference speed).
C*U works well at compensating pitch and lift disturbances associated with turns (to +/- 30 degrees), flap changes, speedbrake adjustments, and thrust changes. The only time that pitch trim input is needed from the flight crew is when changing the desired speed.
When the autopilot is engaged the speed stability of C*U is disabled. Some autopilot modes provide speed targets - those are retained. When autopilot is disengaged the current speed is captured as the initial C*U reference speed so no need for pitch trim input at that point unless you want further speed change.
Your glide slope capture example is correct. If flying level at the desired approach speed prior to GS capture and possible configuration for landing (flaps / gear) there is no need for pitch trim input as a result of GS capture, configuration adjustment, or the associated thrust adjustments. It will behave just like C* as long as speed is maintained. Boeing philosophy is that if speed is not being managed, the crew awareness should be increased by having the airplane tend to pitch up or down as required to capture the reference speed. Turn on the autothrottle and you essentially have a pure C* airplane.