"To be clear then, your objection is that any physical device that seems to add is doing something different from a "theoretical" device that doesn't actually get built."

As long as the domain on which they act is different, they are doing different things. If your theoretical device includes the whole universe as the domain on which it acts, then you generally cannot prove that they are doing different things (Halting problem).

But I do not say that you cannot create an AI that seems to act like a human, and I am not saying that it wouldn't be thinking like a human or that it wouldn't be conscious.