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If you were to attach the front sway bar of a stock bug to the center of the beam, you would then have a Z bar AND a sway bar. It would restrain both wheels in bump and droop, depending on where you set the center position. My rear sway bar is just like that, except it only works to resist droop.

Are you hard mounting the sway bar and not allowing it to rotate? If so then I would agree it is nothing more than a torsion bar but if it is bushed then you should get some compression and droop and work as a sway bar if one side traveling at different rate than the other side. Maybe I am not understanding the last comment.

Lee

First, a "Z" bar is called that because it's mounted at an angle and the links off the ends point in opposite directions so that it acts exactly the opposite of a swaybar (and like a camber compensator) - by definition it would be impossible for any bar, regardless of its mounting bushings, to be both. Yet the factory rear Z-bar also acts as an overload spring when the suspension is so heavily laden that all of the slop built into the links is taken up (under those conditions it's not likely that your primary concern is going to be the finer points of weight transfer in a hard corner) ...this allowed them to make the rear torsion bars lighter, in order to reduce oversteer, without having to de-rate the load capacity of the vehicle - that was the whole point of (and the genius behind) the Z-bar design.

As jhoefer pointed out, the stock front swaybar is not intended to have any mounting points between the clamps at the ends - because of the semi-rigid way that the clamps hold it to the control arms it must be free to deflect along its length - you cannot make direct comparisons between the action of the VW iteration and what's found on most cars, where the suspension motion imparts only vertical motion to the swaybar lever ends, since on the VW the motion of the trailing control arms forces the bar to twist without it needing any center mounting points. If you restrain it to a pivot point on the beam, whether it's free to rotate or not it's going to bind and resist movement of the control arm in either direction - it won't work well as a swaybar or efficiently as an overload spring, but the effect will be less like the former and more like the latter.