Interesting question AlphaZeroOne.
Well I don't think "variable aperture" stacking would be anywhere near as useful as focus stacking, however for an entirely different reason there
may be some merit in trying it. It could possibly be used to overcome (in part) the loss of fine detail caused by stopping down beyond the diffraction limit of the camera's lens. In my case (Nikon 105mm Macro VR lens) image degredation becomes noticeable from about f/13. However IMO it's not really a significant problem until f/20+.
If you're not familiar with the effects of diffraction limitation check out this website tutorial:
Diffraction Limited Photography: Pixel Size, Aperture and Airy Disks
Anyway back to your question:
In the past I have occasionally experimented by taking two different shots of the same macro subject at different apertures. Typically one shot at f/8 focused on the nearest bit
of the most important part of the subject (for example the eye) and another shot at f/22ish, focused on the nearest part of the subject overall. Of course the subject must be very still and ideally the camera should be tripod mounted.
The f/8 shot will have a relatively narrow dof, however the eye should be in focus and the image will not suffer from 'diffraction limit' related loss of detail. This means that the subject's eye will show good detail.
The f/22+ shot will have a much deeper dof but there will inevitably have been some loss of detail in the eye due to exceeding the diffraction limit of the lens.
I have then used CS3 to manually merge the (good detail) eye from the f/8 shot onto the (good depth of field) f/20+ image. However (considering your idea) I think I could probably have used Zerene Stacker (or CombineZP) to merge the two images with better results than I was able to achieve manually.
Bruce