This is my understanding of how things work:
Reporting TCs (Canon I, II & III, Kenko DG, Sigma): A TC-compatible lens (e.g. 400/5.6) detects the presence of a TC through the 3 extra contacts and reports the correct f-stop for the combination to the camera. If the f-stop is above f/5.6, AF is disabled for non-1-series bodies.
Non-reporting TCs, or taped TCs, or TCs with non-TC-compatible lenses: The lens does not detect the TC and just reports its own f-stop. AF may still work, because the camera doesn't know about the true f-stop, and tries to AF even if the combination is outside the specs.
Kenko DGX: Unlike the above TCs, the DGX manipulates the communication between the lens and the body so that the f-stop is always reported correctly for the combination, and so that AF is retained even if the combination is above f/5.6. From your and others observations that f/8 is reported but AF still works, my guess is that wide-open f-stop and used f-stop is reported separately and the camera looks at the wide-open f-stop to determine if it should try to AF.
So you could use the canon TCs on the 100-400mm f5.6 but manual focus only and you would lose 1 f-stop of light with the 1.4x TC so 140-560mm f8 or 2 f-stops of light with 2x TC so 200-800mm f11 lens.
You could still use the lens and canon TCs, manual focus only, but image quality would be hit and you would still need very good light conditions to achieve decent images or gamble with one of the other TCs that doesn't report the TC.