I have the Kenko converter you are asking about. Concerning AF, one thing I can tell you is that it functions without taping the pins, even on a lower-quality body like my 60D, even if your lens then is slower than 5.6.
As far as how it functions with the 70-200, I don't know, but my 60D was very poor at AF with the TC and my Tamron 70-300. The lens more often than not failed to achieve focus and hunted a lot. If conditions are really bright and very contrasty, sometimes it would work.
With it on my Canon 400 5.6 lens, it is also kind of uncertain. The lens won't hunt, it just sits there and does nothing. With full-time manual override, I can get it close to focus and then sometimes the AF will take over and achieve focus. In bright, contrasty conditions, it will sometimes work OK, but it seems very unreliable. I think it might be good to use for situations where you know it will be bright and you need the reach and you have plenty of time - say ducks on a pond. Can't hurt to try it.
Edit: I just reread the thread and see that the lens in question is a 2.8, so the TC would probably work better with that, since you won't exceed 5.6 anyway. I'll leave my posting in place, just FYI.