It depends on the individual lens, but it can actually work opposite to the way you're imagining it.
Remember that if the focal length of the lens is less than the sensor-to-back-of-lens-mount distance, then the lens must be of a retrofocus design. (And that with single-lens reflex designs, that distance is going to be something in the neighborhood of 40mm.) That is, the rear portion of the lens is of a much longer focal length than the focal length of the lens system taken as a whole, but it's looking through a concave window on the world. It's sort of like looking through the security peephole in an apartment door through a telescope. (That's why lenses with teeny, tiny focal lengths have such huge front elements—in order for the entrance pupil of the lens to be visible to the entire field of view, the front element needs to be a whole lot bigger than the calculated aperture would suggest.) So at the shortest focal length of the entire lens, the rear segment may actually be configured to be at its longest focal length, and thus have the narrowest light cone behind the lens and the smallest image circle the lens can produce.
There can be any number of ways to achieve the same focal length range, so the pattern of variation in image circle size changes may be different for different zoom lenses of the same range. Browsing through the lens reviews at photozone.de, for instance, and keeping an eye only on the vignetting charts, you'll see that vignetting problems can occur at both ends of the zoom range, or even be worst in the middle of the zoom range. Almost every APS-C/DX zoom, though, displays significant vignetting wide open on the camera it was designed for over most of the range, and that doesn't take into account hard mechanical vignetting outside of the designed image circle, just the slow optical fade. You can always test the image circle off-camera by zooming while projecting the image onto a piece of paper. You're likely to see size changes, but not necessarily where and how you'd predict.
I don't think it would be worth anyone's while, really, to unlock the next crop size up between, say, 42 and 44mm and then again between 58 and 63mm on a given lens because the image circle was slightly bigger in just those ranges—it would just lead to user confusion and consumer complaints.