Besides the 400/5.6L, my on-the-road setup is 300/2.8L IS MK1 + stacking of Canon 1.4x II and Kenko 1.4x to get myself ~600mm (588mm to be exact), and the focus is just as fast as using only Canon 1.4x II. The photo still ends up fairly sharp with minimal degradation in crappy lighting/weather. The only penalty is my Canon 7D is about +1 EV off, so you have to compensate by -1 EV if you're shooting in the auto modes. For manual mode it's irrelevant.
Here's an okay flight shot of a Pileated Woodpecker, and I'm sure I will still get similar results with my 400/5.6L as these woodpeckers are not easy to photograph:
Here's a Common Merganser male I shot recently with lighting behind my back:
On the other hand, if you have a slow prime, i.e., 400/5.6L, either tape the pins of the Canon TC, or you can try use the Kenko 1.4x, and the focus will work at f/8, but slow and hard to detect contrast! Here's an example of a Snowy Owl I shot in early spring:Moral of the story, use teleconverters on fast primes!