For those who want more of an explanation than "No it doesn't" - because the sensor-core is present in the Snapdragon 400 - the reason the 'Hey Cortana' feature is not available in phones with the S400 is because of which sensors are actually available to be used without powering up. Before anyone replies "That's not quite how it works", I know my explanation is simplistic, but I am trying to make it comprehensible.
With the S800, there are sensors that detect movement, location and sound, which can be accessed without using power. This enables these to be used by apps, 24/7, without draining the battery. With regard to the sound element, specifically, it can be programmed to listen for a specific sound and wake an app; and that 'sound' is 'Hey Cortana'. As many have pointed out, the S400 does have sensor-core, but this does not include the sound sensor. That is why this feature will not be included in any phones that do not have the S800.
I have heard mention (though I have no idea of its validity) that MS are trying to enable this functionality in the S400; but quite how that is possible, given what I say above, I do not know.
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