"Does the little wireless remote Canon RC-6 do the autofocus work or just trigger the camera?"
It just triggers the camera. The lens does the focusing. When the camera is triggered, it tells the lens to do it's thing.
BTW, it is basicllya line of sight controller.
In other words, yes, the camera will autofocus the same using the RC-6 as it would pushing the button on the camera.
I use my RC-1 all the time, and have been for 7-8 years now. They're great little triggers. Even though my camera has Wifi, and I have radio triggers, sometimes it's just easier to pull out these little remotes and deal with the line of sight limitations.