Well now, I just had an interesting thought.
What if we take a conversation filled with "I" and remove them all? Also all the "you?"
I can see an intelligent entity functioning perfectly normally without such references in it's language.
So suppose we take such an entity, and add a chinese room like interface on top
of it that, for every statement to and from the entity, it parses the
statements and inserts the proper grammatical form of "I" where necessary.
Could that entity be a p-zombie?
Well, don't confuse the word with the concept. If you simply elimante the words, the test question should simply translate into the new pronounless language. Forbid me from using "I" and "you" and I can still talk about yy2bggggs and rocketdodger just fine; or, closer to the heart of the matter, "the one typing" and "the one reading".
If you want to start removing the I
concept (at particular layers), then
that is where you need to start slicing. Knock out my ability to recognize you as a separate agency and I no longer have the same concept, though I may very well still have a feeling of control that I cannot explain. Knock out my sense that I can control actions and you've cut deeper, though I would caution you that at this point you're starting to severely interfere with the "normal working" of this machine. For lighter touches, you can mess up my ability to conceive that the thoughts floating in my head are "mine", or any of a number of similar attacks--and at that point, you no longer need to hypothetically imagine entities, for there are plenty of real ones to study.
This sort of thing might change your question a bit, but I'll offer this general opinion. Having an "I" and having a concept of an "I" are two different things, and neither comes for free. Furthermore, there's nothing special about the Chinese room IMO; it has the same requirements for having either that biological entities have.
I agree with calebprime though--this isn't what p-zombies are supposed to be. They're supposed to refer to entities that lack the "raw feel" of experience, whatever that is. I recognize that you find this incoherent, but I don't see that as a valid objection to the definition. It's still supposed to refer to it. If it happens to be incoherent, it's simply incoherent--reformulating it coherently is still reformulating it all the same.
ETA: Just to note, however, there are various sensations tied to the "I", and I'm not
entirely sure about the last paragraph, depending on what "whatever that is" is supposed to be for p-zombies.