Yes, it will work, however their are some big caveates that probably make it not worth it.
It will be an f/11 lens at the full 800mm focal length as a result of losing two stops of speed from the teleconverter. This means PDAF will be unable to function and you will need to focus manually or use live view and contrast based AF.
Additionally, you will be focusing through a very small portion of the center of the lens. An APS-c sensor starts out only using a portion of the center of a lens and a 2x teleconverter cuts this down by another 1/4. The 100-400L simply isn't sharp enough to avoid getting a loss of sharpness from using that small of a portion of the lens's field of view.