Are you shooting jpg or RAW? Each RAW has a small jpg attached to it for rapid viewing on the back of the camera screen, for example. But, ultimately, a RAW file is not affected by "in camera" settlings. So, if you are shooting RAW, in camera adjustments have very little effect.

If shooting jpg in camera, then yes, tweaks in camera will adjust your final output.

As for the 2xIII with the 100-400 II, which camera body do you plan to use? With a 1.4x III extender, I know the 5DIII would AF with center point only at f/8, but several newer bodies will AF at multiple points. However, add the 2x III on, and that is actually now an 800 mm f/11 lens. I just checked, and my 5DIV would not AF with the 2x III 100-400 II combination.

However, if you shot MF with this combination, you may be able to compensate for some of the AF loss. Of course, IQ lost is never regained, but sharpening and playing with contrast a little would likely help the images. Too much and the photo can look processed. I know that I traveled with the 70-200 f/2.8 II with the 2x III and process those pictures to the point I was happy with them.