It can be done, however when the fisheye is "unwrapped" or "re-mapped" for the correct perspective, you will not be able to see anything below lens-level, which is approx. just above your knees in the picture yu posted above. That means you will not see the ground or floor in the panorama.
There are lenses that capture FOVs greater than 180 degrees for one-shot spherical panos... in fact Coastal Optical Systems at one point was researching/prototyping an ultra-wide lens (around 300 degree FOV) for Ipix, but I'm not sure if they ever made it into production.
Lastly, you'd really need a high-res DSLR to do it justice... A one-shot pano requires all the image info of the whole scene to be crammed on the cameras image sensor, rather than dividing it up between 2 or 3 exposures. By nature, this greatly reduces the number of pixels you have to work with, which will be visible in the final pano as lack of detail and clarity.
For one-shot panos, I'd recommend a system like BeHere, etc., which captures cylindrical panos using a convex morror. You can still view them with a spherical viewer to correct the wierd geometry (looks more 3D as you pan).
It's great to experiment though, and try new things. That's the beauty of this type of photography... there's a million ways to twist and turn the process and, once in a while, we end up with something really cool and new. I love that kind of inventive spirit.