lens - Will I not be able to AF with a 2× teleconverter?

My setup is a Canon EOS 600D with a Canon EF 70-200mm f/4 L (non-IS), and I really want to buy a 2× teleconverter (1.4× is too short). I have done a lot of research, but I can't wrap my head around this.

Now, I understand that I will lose AF after f/5.6(?) with this body, but does that mean that I need to use my hand for manual focusing? I normally never use all the AF points. I use the central AF point, half-press the shutter button, then move my camera to where I want, keeping my focus locked and taking the picture. Will this way of focusing still be possible, or does this too count as AF?

Answer

You will have to manually focus by moving the focusing ring on the lens.

Using the center focus point to focus and then recompose is still considered autofocus. Even if you have manually selected which autofocus point the camera uses, the camera is still focusing the lens, not you.

You'll also lose more image quality with a 2X than with a 1.4X. This will be most evident in terms of CA and flare when shooting into bright lighting. You'll see much less image degradation when the brightest light source, such as the sun, is behind you.

In general 2X teleconverters and extenders are only recommended for f/2.8 or faster lenses. Some bodies (most of the 1D series, the 5D Mark III, and the 7D Mark II) can use the center AF point with f/8 lens/extender combinations. But the narrower PDAF baseline of the APS-C cameras makes this much more difficult than for their full frame counterparts. The FF 1D X Mark II and 5D Mark IV can even use many of their AF points with an f/8 lens/extender combo, but even those high end models don't perform AF as fast or as well as they do with a faster lens.

For more on how f/8 combinations may or may not work with third party TCs with Canon EOS cameras, please see this answer to Will the Canon 5D MK II with 100-400 1:4.5-5.6 work properly with Kenko 1.4 converter?

For more on the variety of TCs please see this answer to How do I choose a teleconverter for my Tamron 70-200 f2.8 and Canon camera?