In that case you've basically just created a split-brain situation (I mean like the actual phenomenon of someone who's had the main part of the connection between the two hemispheres of the brain). There's one system which is the man and the rules that he has internalized, and there's what the man himself consciously understands, and there's no reason that the two are necessarily communicating in some deeper way, in much the same way as a split-brain patient may be able to point to something they see in one side of their vision when asked but be unable to say what it is.

(Also, IMO, the question of whether the program understands chinese mainly depends on whether you would describe an unconscious person as understanding anything)

I also can't help but think of this sketch when this topic comes up (even though, importantly, it is not quite the same thing): https://www.youtube.com/watch?v=6vgoEhsJORU