However, would the new Canon Hybrid CMOS AF III system (as seen in the Rebel T6s / EOS 760D and T6i / EOS 750D) enable AF down to f/11 (like the dual pixel CMOS AF does in the EOS 70D and EOS 7D Mark II) in Live View mode?
With Canon, AF specs based on the maximum aperture of the lens used are always applicable to PDAF (viewfinder) usage and are not applicable to CDAF (Live View) usage.
Although a lens with a wider aperture, as well as a well lit scene, make it easier for imaging sensor based autofocus to function quickly and accurately, in general most cameras can usually autofocus successfully with lenses having maximum apertures narrower than what their corresponding PDAF sensors can handle. This is mainly due to the differences in the way PDAF and CDAF work.
Many Canon cameras automatically disable, via firmware, the PDAF system when used with a lens that reports to the camera that it is limited to a maximum aperture smaller than f/5.6 (or f/8 for some top tier models).¹ Those same cameras do not automatically disable main imaging sensor based CDAF and will attempt to AF with f/8 lenses or even f/11 lens/teleconverter combinations. Sometimes they will even succeed.
¹ Even older models that don't automatically disable AF with an f/8 lens will struggle to be able to successfully AF at f/8 unless being used in very bright light on a high contrast target. This same models can often AF via sensor based CDAF with f/8 lenses.
According to the T6i manual:
AF Operation and Maximum Lens Apertures
Maximum Lens Aperture: f/3.2 - f/5.6
With all AF points, cross-type AF sensitive to both vertical and horizontal lines is possible.
Maximum Lens Aperture: f/1.0 - f/2.8
Besides cross-type focusing (vertical and horizontal lines detected simultaneously), the center AF point can also perform high-precision, vertical-line sensitive AF. The remaining 18 AF points perform cross-type focusing, as with the maximum aperture at f/3.2 - f/5.6..
So the answer is: f/5.6 is the maximum aperture for auto-focusing on the T6i.