Whether the camera can focus to take an image through the lens is one issue. It doesn't look like this type of lens is used for image-taking. Googling around, I can't seem to find a single image taken with one. This type of lens looks like it's used for laser focusing or magnification. Not for photography.

But if you can use it for photography, then the problem comes when you want to stitch the images together. You'd have to know how to map out the lens properties and distortion characteristic for the stitching software you're using. And get your software to use your lens profile, because they're mostly only preset to use rectilinear or fisheye lenses for this task. Again, this isn't insurmountable, but would probably mean you can't use PhotoSphere, ICE, Photoshop's Merge or AutoStitch to do this. You'd probably have to use a PanoramaTools front-end, like Hugin, and you'd have to have the appropriate test chart and lens profiling skillz to create a profile specifically for your lens/camera combination.

Also, just my guess, but I really don't think you'd be gaining a lot of image quality over a fisheye adapter (I've seen surprisingly good results from those cheap adapters), and chances are that the more extreme distortion at the top and bottom of the frame would probably still require at least zenith and nadir shots if you're REALLY worried about image quality.