You could bet that if it did, Sawgrass would try to claim a patent on it.
I know that many of those printers use a special cartridge containing layers of a cellophane type material. The printhead is heated by thousands of individual elements, that release the dye into the paper, by varying amounts.
Not sure whether you could then sublimate the image out of the resultant paper image, or whether the dye is permanently sealed in?
As they say, there is only one real way to find out.