Ah, Chinese room questions.

The system that replays the sequence can be anything, including a human with pen and paper.

Does the system truly exhibit the original consciousness sequence, in addition to the human's existing consciousness?

Yes, assuming that the measured consciousness sequence captured the essential elements of the original consciousness.

To "see" the original consciousness in this system you must adopt the correct context; the context that resolves the consciousness abstraction within the system. From that context you will not see the human. If you see a human following instructions and making notes, you will not see the consciousness he is generating.

Consider a chess program playing a game against itself. If we glance at the monitor we would see the game as it progresses. If instead we only could examine the quarks that make up the computer, we would be completely blind to the chess program abstraction.