Tile floor installation on top of hardwood
Yes. Just make sure you use fiberglass mesh on top of the backer and use a good quality polymer modified mortar to install the tiles.

Backerboard subfloors are a cheapout way of avoiding the installation of a proper lath and mortar base (there is simply no comparison). If you choose this route, there is nothing to bind the floor together (which prevents cracking). using a fiberglass mesh interface membrane will help to act as a mechanical binder for the tile floor to be laid.

The use of polymer modified mortars instead of simple cementitious mortars makes a huge difference in how well the wet "stick" of the tiles makes sure there is a high percentage interstitial bond between the tile and the subfloor. This makes sure that once it sets up, the tile has no ability to move in relation to the mesh/backer assembly. This ensures that even if there are minute voids between subfloor and the backer--the footprint of the tile is spread as wide as possible through the backer to the subfloor. The intention of this approach is to remove any chance of decoupling of the tiles.