westhawk;
Re, "I've heard this technique referred to as "looking through the FD" too."
Yes, that's exactly what it was/is. That applies today, even on Airbus aircraft.
The best demonstration of this phenomenon is (in the sim), flying a raw-data ILS in poor vis or at night with a bit of wind/turbulence.
While it can be done quite well, if one isn't practiced at it, keeping the LOC and GS centered presents quite a challenge.
However, with the FDs on, one "subliminally" sees the movement of the FD and "anticipates" in the manner you described, making the job a lot easier. One is still "flying through" the FDs, focusing on the small pitch, roll and heading changes as they affect the ILS indications but the FDs are of significant assistance if one uses them this way.
Again, the Airbus FDs are indicating what the autoflight would do if engaged and so appear (but are not actually as this is just software, not a human being!), "anticipatory" in that the autoflight system (and therefore the FD system) senses imperceptible deflections of the ILS and the actual PFD indications are smaller than may be initially perceived by the PF - but the FDs respond and their deflections are visible and so can help maintain the flight path, without "leading" the pilot on a leash...so to speak.
"Looking through" the FD requires time to learn; it doesn't mean one is ignoring the FDs, it means that their indications are appropriately "psychologically placed" and used at various learned levels of awareness. In my view they aren't, in the end, necessary, but they are an enormous aid in many though not all circumstances.
One tends to ignore the FDs, (looking past them and not just through) in transient moments of energy changes where the FDs do not know what is coming next but the pilot does, or should! In my view, the most important example for understanding this is the AF 447 accident.