One can do various interesting thought experiments with such an object. The contexts where this might be useful include the abstract topics such as "Hard Problem", technological singularity, or uploading, and more practical topics, for example, something like "if I could change a way I am [reading mathematical papers/writing computer code/...], how would I want to do that, and what would I want to feel in the process of doing that".
1) In context of the "Hard Problem", I think the ability to achieve a situation like this would be the best test of our understanding of the "Hard Problem" (and would make the subjective realm much more amenable to tests and experiments).
Here we must assume that a sufficiently non-trivial part of a given subjective personality is associated with the artificial device (and, for example, when the body gets sleepy, we are likely to observe the shift of the subjective towards what is mostly running on the artificial substrate; and if the coupling remains during sleep, we might get some version of lucid dreams as part of the overall activity).
2) In context of mind uploading, this seems to provide a much saner approach that what people usually discuss; an example of an approach along these lines is here:
3) In more practical contexts, the question what would I want to feel in the process of doing [A/B/C/writing computer code/reading mathematical papers/...] makes sense on its own and might be useful to consider.
4) We can also ignore the fact that we don't know whether one can use an ordinary computer as a device coupled in this way to a human brain, and even if the answer is positive, that we don't know what would it take to achieve a coupling like this (both depend on what the answer to the "Hard Problem" really is), and ignoring our lack of knowledge here we can try to meditate on how we might want to program the computer to do this or that, if such-and-such layer of the processing were conscious. (Ignore the fact that without further progress on the "Hard Problem" we don't know how to distinguish between conscious and unconscious processing; and decide that we have some freedom is designating some views into the running system as conscious.)
5) One also has some freedom to run things slower or faster in the artificial device, although if one wants to preserve coupling with the biological there are probably some constraints. When I start to think/introspect about accelerating some parts of the train of conscious thought relative to other parts, what I mostly feel is cognitive dissonance, so I am not sure whether this direction of thinking is fruitful (в этом месте, оно несколько сносит крышу).
I am not sure how much of the above makes sense, but I was thinking about this topic during the previous week and have not lost interest, so I decided to share this.