With the official launch date of the new Canon EOS 1-DX approaching, Canon has published a guide to the camera's AF settings. I'm hoping that the EOS-1DX isn't the kind of camera that has an AF system that's only as good as the user can set up (and it looks like it from this manual). There's no mention of autofocus being operational at an effective aperture of f/8, a feature that the rival Nikon D4 offers (which is useful when using a 600mm f/4 and 2x converter together - a fairly typical scenario for many wildlife shooters).
Indeed, Canon circumvent that point directly but they do state on page 39, when referring to the number and placement of of cross type points used by f/5.6 lenses "Many lenses with EF 1.4x or 2x Extenders, and compact zooms fall into this category. With lenses having maximum apertures slower than f/4, high-precision AF is technically not possible, but 21 AF points in the central area still provide cross-type AF coverage, and the wide-area coverage from all 61 AF points remains available".
From that paragraph, the 600mm f/4 and 1.4x converter will work as an 'f/5.6 lens' (albeit without 'high precision AF') but it appears confirmed then the EOS-1DX will not perform AF with any lens / telecoverter combination with an effective f/8 aperture. All the same, it will be interesting to see just how well this camera performs with effective apertures outside the AF sensor's optimum sensitivity range, especially when compared with the Nikon D4.