I think that the rule of thumb for Canon lenses is that for 1 series camera such as 1D4, AF cease to work with an extender once the maximum aperture goes beyond F8. For cameras other than the 1 series (such as 7D and other cameras), the maximum aperture is F5.6, beyond that AF will cease to work.
As a result, if you have a 1D Mark III or IV, you can bet on having a 300mm F4 with 2x extender as in this case, the maximum aperture can be attained is F8. Yet the AF speed may be slow. Other than the 1 series cameras, you can't use the 300mm F4 with a 2x extender. In this case, you can only use a 300mm F4 with a 1.4x extend to obtain an F5.6 maximum aperture.
And I think that Canon 100-400L has a better photo quality over the Sigma zoom.