Not an expert here, but my understanding is the tile and your base will expand and contract differently. If you thinset them together, somethings gotta give and that something will be your tile job. I would say the answer is no. At least I wouldn't. The bottom edge of the tiles shouldn't rest on the base. Leave about 1/4" gap along the bottom and caulk that area.
Where does your hardiebacker end? Does it butt up against the flange, or does it overlap it?