In the P2V7 (aka SP2H or 4eng Neptune) you could engage the autopilot in baro hold and then quickly gain up to 12kts indicated (190 to 202 rings a bell) by trimming a load onto the elevators via the autopilot's electric trim-wheel (with auto-trim declutched).
My theory on that was that it was loading the control surface and streamlining the trim-tabs - thus reducing trim drag. It's also possible that the resulting airplane attitude was more streamlined (and thus benign) in terms of the Thrust-Weight/Lift-Drag couples (and their equilibrium position).
It wasn't an induced static error either, because the NAVS would always confirm the extra TAS. I mulled over this for ages way back then and tried to factor in what else might have been happening with the varicam (variable camber tailplane horizontal stabilizer). Never did find a bottom line there.
Trim tab position does make a difference. In an MB326H you could hold the nose off down to ultra low speeds (for aerody braking) if you ran the elevator trim full nose-down after touchdown. It was then acting as an elevator augment.....and boosted elevator effectiveness tremendously.