First off there is no reason why you can't use a panorama head mounted off the centreline axis of a tripod as the axial center of revolution for the camera is the critical component.
However there are a few practical restrictions on the above statement, namely:
The panorama head still needs to be correctly oriented with respect to the horizon, that is level in the horizontal and vertical planes so that the images will correctly line up.
Lens choice will be critical. If a lens has a fairly wide field of view the tripod and quite likely the off axis bar will be visible if you need to shoot over them. see note 1
Finally there's the problem of stability. In order to use an off axis panoramic setup you'll need a pretty hefty tripod, quite possibly with extra weights to ensure a stable footing. The position of the off axis panoramic setup relative to the tripod legs may be critical for stability in some cases.
Off axis panorama shots would ideally be limited to a 180 to about 220 degree hoirzontal coverage with most lenses of less than about 80-100mm focal length in order to avoid having the tripod and or off axis mounting bar/pole showing up in the images.
My interpretation of the question is that the tripod mount of all non-SLR digital cameras have the tripod mounts off the axis of the lens. So how do panoramas taken with these cameras turn out?
My experience is that the panoramas can turn out very well. Distant objects are not a problem. The problem is with alignment of close objects eg the tiles on the floor.
However, this can be blended away using the programs like Panorama Tools with Photoshop. It is a powerful combination although the learning curve is high and it is labour intensive. With Panorama Tools, you can adjust tilt, raw and pitch so it is even possible to shoot without a tripod. However, blending is easier when a tripod is used.
Have a look at a proper panorama head for a digicam, they have an adjustable bracket to compensate for the off axis lens to camera tripod mounting socket.
Problems with off axis lens to the panoramic head rotational axis vary with the total number of shots in the panorama, the angle of coverage of the lens and the total angle being covered by the final combined shot.
Using panorama tools in Photoshop is one solution, but a far better solution is to do the job properly at the camera in the first place.