to an extent, yes
but: what is the point of HIIT, in a semi-fed state? are you trying to boost your energy level/performance then, at the expense of the "fat-burning goodness" you state is the goal? seems contradictory, don't ya think?
key words there being "would suggest"...don't misinterpret this as "universally emphatically proves"
that said: yes I am a fan of occasional shifts in the macro/micro loads, to reach an end goal (and always with the intent of body composition purposes)
it all boils down to what you are trying to accomplish, but it seems to me you are getting caught up in minutiae at the potential expense of your own progress and goals
why not just run fasted HIIT rising, then follow with whatever nutritional profile you wish to embrace that day then?
this, would be fat-burning goodness, assuming everything else is done properly and optimally...