Maybe...but unless someone has actually tried it, you can not be sure.
If you ask Nikon, they will refer you to Sigma for an answer.
Some lenses made by other companies have to be modified before they will work on a digital camera.
You should contact Sigma for an answer.
If it does work, those Nikon cameras you mentioned will see the 28mm-200mm lens as being 42mm-300mm.
This is due to the CCD sensor on the Nikon being smaller than 35mm film. You use a multiplier of 1.5 to determine how the Nikon will see the focal length of a lens.
I have a Nikon SLR film camera,(F65) with a Sigma 28-200 mm lense, now I am looking for a digital camera to replace it, and I am interesting on the Nikon D200 or D80, my question is: can I use the old Sigma lense on the new Nikon D200 or D80?