Question about Canon EF 2x III teleconverter

In theory, yes, according to this link https://www.canon.co.uk/pro..., but there may indeed be problems with light and therefore autofocus. We'll have to see in practice, depending on the conditions.

It is compatible but the autofocus does not work

Compatible with the camera, presumably. I don't know the lens. I no longer use the extender.

I have a 5D Mark IV and the same lens. After a few days I swapped the extender for an EF 1.4x because the autofocus didn't work with the 2x. The reason: the 2x increases the minimum aperture so much that the autofocus no longer works. I am very happy with the 1.4x, however.
Here is a link to a forum that addresses the topic:
https://www.dslr-forum.de/threads...

Good light!
Urs

If the bayonet (i.e. the interface) fits, then yes. You have double the focal length and half the aperture. However, your 400mm with extender will not achieve the same image quality as an 800mm. At least that's my experience