Yes—this is commonly done with a separate nadir patch shot rather than trying to stitch everything at once.

A practical method is:

1. Shoot the main pano on the tripod as usual.
2. Take one or two downward shots on the tripod for reference.
3. Remove the tripod and shoot a handheld nadir frame, or reposition the camera so the entrance pupil/viewpoint is as close as possible to the original position. Some people use a measured reference (for example, a hanging tape to a marked ground point) to place the camera accurately.
4. In PTGui, first align and optimize only the tripod-mounted images.
5. Add the handheld/repositioned nadir image afterward, set control points manually if needed, and use masking so only the useful central ground area replaces the tripod/pano head.
6. Keep the patch area flat/simple if possible, and avoid casting shadows from yourself or support.

The key is that the nadir patch should be treated as a cleanup image, not as part of the initial global stitch. Shooting it slightly off to the side can also help avoid shadows and obstructions.