I just tried my 5D2, Canon 50/1.4 and Kenko 1.4X Pro 300 DG (not DGX). The combination does not report EXIF correctly and there is some hunting at times. I'd say the image is unusable wide open, not matter what size you intend to display/print. Closed down a stop the centre sharpens up a bit, but edges and corners are very bad. I'd say you need to close down by at least 3 stops to get the corners passable, but still not great. That's f/4 reported, f/5.6 actual. The DGX version might well do better, in all respects, but I really have no idea how it performs. Optically it is supposed to be the same, but there is some jiggery pokery to improve EXIF data handling.
However, it might be that my 1.4X is not a great example. It works perfectly well with my 100-400 at 400/560mm, but is absolutely abysmal with my 135/2L, even when stopping down a few stops, and that's on a 7D, so corners not even put to the test.
I think you're going to need at least one more opinion about the combo, because my experience may well not be representative. It might also be worth noting these remarks from the Kenko website....
The PRO 300 family are designed specifically to be used with prime telephoto lenses of 100mm or above, such as 300 mm f/2.8 lenses, and work best with telephoto lenses of 200mm to 500mm. The PRO 300 can be used with telephoto zoom lenses as well as prime lenses. However, Kenko does not recommend them for zoom lenses that have a range starting under 50 mm.
I'm considering buying a Canon TC, as a replacement, which hopefully will perform far better across the width of the frame on a wider range of lenses. It would be quite nice to be able to turn 135mm at f/2 into 189mm at f/2.8 without needing to carry a whole extra lens around. At the moment I am unable to do that successfully.