First of all, most cases are designed with the Lightning to 30-pin adapter cable in mind, which has a slightly wider plug:
But I went ahead and measured it, just for you:
The smaller plug from the USB Lightning cable is 8mm wide, while the blade is 6.5mm wide.
If you now take the known width of the blade and compare it to these measurements:
The plug turns out to be 8mm wide, so it has the same dimensions as the one on the USB cable. From that I deduct that it'll fit any case, unless you have some rugged case that's remarkably thick on the bottom.
The way I know Sony, they were so smart to use the exact same dock assembly on the smaller alarm clock as well. At least someone at Sony had the brilliant thought that people put cases on phones that scratch easily, and that you don't want to remove your case to dock it, that's worth a lot already.
Try it out, if it doesn't work with your case, you can always return it without restocking fees. Just let us know the result.