adherring hardybacker to plywood?
I reckon you should be OK, although most standards for tiling walls over HardiBacker (cbu) says half-inch. But this is almost decorative, like a backsplash - not a floor after all and therefore the requirement that the cbu and the subfloor (plywood) and the tile be 'integral' - that is cemented in place to make it 'one', to give it added support and resistance to flexing - is not there. It's a wall... So adhesive+screwing the plywood?: OK. Screwing the cbu?: OK.
Your modified thinset behind the tile will 'flatten' the wall it out fine. Mastic, or an organic adhesive is fine too, in this application.