Hi Folks

Looking for some advice hopefully from someone with first hand experience.
Currently use my 100-400 mostly for motorsport,, have loved the lens since I first bought it, I find it reasonably sharp and easy to use. However most of the time am also carrying with me a 24-105 and even include the 100 macro just in case of low light situations. Thinking about carrying one lens only in most cases and have been interested in the 70-200 for a while especially after seeing results and reviews regarding its sharpness,, it looks like a brilliant lens.

What I'm considering is combining the 70-200 2.8 IS II with a 2x III Entender. This setup would cover the range that I mostly use, rarely use wide angle or even get close 50mm.
Just wondering how much the extender would interfere with picture quality?
Am hoping others use this set up and advise or at least pass on their experiences.