If you define waste heat, neural patterns, and so on as "output channels" then sure, we can say you only interact via I/O (although the line between I and O is fuzzy enough and your control over the O is small enough that I'd personally object to the distinction).

Also, even with perfect control of your own cognition, you would be restricted to a small subset of possible output strings. Outputting bits on multiple channels, each of which is dependent on the others, constrains you considerably; although I'm not sure whether the effect is lesser or greater than having output as a side effect of computation.

As I mentioned in a different context, it reminds me of UDT, or of the 2048 game: Every choice controls multiple actions.