I wouldn’t recommend that approach. I get better results both IQ and AF with the 2x (no internal 1.4x engaged) than the internal 1.4x + external 1.4X TC III. You may find different result if you experiment with the lens, but this is pretty consistent from testing and use. I have even tired the 2x + 1.4x internal engaged, but that gives you f11 and you loose autofocus even on a 1dx II. The image wasn't horrible, but I wouldn't use it for anything other than a website. Either a 2x or 1.4x you would have to swap it out if you wanted to drop to 200-400. On safaris other than the Mara or Serengeti, I usually find that the 200-400 + occasional 1.4x enabled 280-560 gives me more than 90% of the shots I want.It needs only a 1.4xTC popped on to give 400-800mm as it has an internal 1.4xTC.
I can believe that, especially as the digital picture found better IQ at 560mm with an external 1.4xTCIII than with the internal. https://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=764&Camera=979&Sample=1&FLI=4&API=1&LensComp=764&CameraComp=979&SampleComp=0&FLIComp=6&APIComp=2I wouldn’t recommend that approach. I got better results both IQ and AF with the 2x than without the internal 1.4x engaged than the internal 1.4x + external 1.4X TC III. You may found different result if you have used the wins.
Believe me, I understand and I have seriously considered selling the 200 - 400 for another long lens solution. I have tried the 400 DO II, 500 II, 600 II and everyone below but I love the versatility and quality of the 200-400. I use my 100-400 a lot, but it can't match my 200-400 especially when you pop on a 1.4x TC III. I have 2 more safaris scheduled before I focus on other areas and will probably sell the lens after the last trip. My second favorite spot is the Western where a 500 or 600 + converters is a better solution because of the long distances. I am also of the theory that much beyond 600mm atmospherics can start to play a role in image quality. I don't do birds very often because I have extremely bad eyesight.I understand that 200-400 can be a great safari and sports lens but for me who shoot birds it would be a heavy burden. My 400DOII weighs 2.1Kg and even my 500II weighs less than the 200-400 and is a stop brighter.
I'm not sure that it does, but it's possible that this allows more elements to be used by providing more space. It also may be easier to design a TC that doesn't have to fit into an existing optical path (ie, by changing the distance from front element to sensor it may be easier to complete the optical path rather than fitting into a specific space). Those are just guesses though...How does that help?