(737 classic, but this should apply to all airplanes, I guess),
Nope, it should apply to all aeroplanes with irreversible controls.
A great many aeroplanes with reversible controls will not self-centre without flying speed, nor should you expect them to.
Having said that, this really applies only to the smaller aeroplanes that I work with (up to Islander size mostly), I believe that the last airliner build with reversible controls was the Comet IV.
By reversible, I mean that without power, applying a load to the control surface will also move the inceptor. By irreversible, I mean that any such feedback is non-existent or artificial.
Presumably any large aircraft doing control checks before main engine start has either ground hydraulic power or (more likely) a running APU driving the hydraulics and electrics (pretty much essential I'd have thought since you'd want power to the ground steering and brakes wouldn't you?).
G