Just for the heck of it, I set up my 1D MK III on my back porch when we had a clear day last weekend and tried the 100-400mm L on Mt Spokane which is about 8 miles distant. I knew the photos would not be picture perfect, there is 8 miles of air to distort the image. I was suprised that those with TC's came out as good as they did.
I think the results show that you need to be close, but also that TC's work better than I expected as long as there is time to manually focus.
I used aperture priority, f/11, ISO 800, shutter speeds varied from 1/2000 to 1/3200. Even in good light, there is noise at ISO 800. The camera could not reflect the aperture value properly with two TC's, but t did reduce shutter speed to compensate so the exposures were ok.
I focused on a television tower, the same one my wireless internet provider uses. I used live view on the the shots and a wireless remote to help keep vibration down. I also used as fast a shutter speed as I could. I tried turning IS off, but results were better with it on, so all the 100-400mm images have IS turned on, even though it might not have worked with the stacked extenders.
First, a shot with a 50mm lens. On a 1D MK III its slightly telephoto, but gives you a good idea of how far away the mountain is.
Next, a view at 400mm.
Now 560mm (with Canon 1.4X II TC)
Now 800mm (Canon 2X II TC) Manually focused using liveview.
Finally 11200 mm with the 1.4X and 2X Stacked and manually focused using liveview.