The Torah makes much about our Free Will, and our uniquely G-d-like nature and potential behavior is framed by many of our sources in terms of that Free Will.
Can a Philosophical Zombie have free will? I think by most definitions, it can't. After all, free will means being able to take in one's thoughts as inputs, contemplate them, and decide an outcome. But a zombie has no "I" inside.
That "I" inside is the ruach memalela, the speaking spirit, that appears in Unqelus's translation of the creation of Adam in Bereishis 2:7. Not "only" a spirit that speaks to others, but one with an internal monolog. This is how the nishmas chayim (living soul) that Unqelus is translating is the same thing the gemara, the Zohar, and rabbis since associate with free will. (E.g. Seforno and Meshekh Chokhmah ad loc.) It being able to take its own thoughts back as input and make decisions about our decisions that we can even speak of having a "will".
Both via that internal monolog and through being aware of experiencing qualia.
(Experiencing qualia: A quale is the difference between a Mary the colorblind scientist knowing that a rose is red, and seeing a red rose and experiencing its redness. It is also the topic of the late-night chat in many dorm rooms, "How do I know that what I see when I see red isn't what you would call 'blue'?" In other words, since you cannot speak qualia, how do you know that both of us have the same quale for red? Anyway, back to to the show...)
Our ability to experience qualia is what Aristotle called "imagination". Not just limited to our current use of the word "imaginary", when we put together remembered qualia into something we didn't experience. And this idea enters the conversion of rishonim as "koach hadimyon" (the power or potential of being able to make likenesses). Rav Yisrael Salanter aligns seikhel (thought), the monolog, with the yeitzer hatov, and the koach hadimyon with the yeitzer hara, in the opening of his Igeres haMussar.
So, a zombie doesn't have a soul, it doesn't have an internal "I", neither the monolog nor the koach hadimyon necessary to be a ruach memalela, a being with free will.
Mal'akhim and sheidim could be zombie-esque. As we don't expect either to have free will. Intellects without free will might be zombies, or at least might have a theoretical zombie counterpart.
The other question would be whether it is possible to come up with the same behavior as a human being without free will. And without just saying Hashem makes sure to duplicate what the person's decision would have been had they have free will, since that isn't libertarian anyway.
And this is where I question the whole thought experiment. It presumes that just because we can imagine a brain can produce the same "outputs" / behaviors without consciousness, that such a thing is actually possible. I would argue it isn't.
For example, there are two ways to think through the question “Does an elephant have hair?”
The seikhel way of thinking: Elephants are mammals, all mammals have hair, and so unless elephants are the exception to the rule, they must have hair. Elephants are well known and discussed animals. Could they be an exception to the rule and I don’t know it? Nah, they must have hair
The koach hadimyon: I can remember elephants I saw, or that I saw pictures of. The detail may be blurry, so you may have to manipulate the picture a bit. Finally, a version of the picture which has a tuft of hair at the tail, maybe (if my memory is good) some downy hair around the eyes and ears, strikes me as the most familiar, the most real. And again I could reach the conclusion that elephants have hair.
To say that zombies are thing is to say that it is possible to make something that always reaches the same conclusions while working in tokens that represent ideas. That could work for simulating seikhel, but is it true that there are NO decisions rely koach hadimyon? In practice, we make many decisions only basedo on dimyon. R Yisrael Salanter says they tend to be bad ones; you need bicameral thinking to be healthy. ("Bekhol levavekha - bishnei yitzrakha / 'With your endire heart' -- with both yetzarim [good and evil]"?)
Every time we follow a desire, even a good one, we are following our mental image of what satisfying that desire would be like.
I simply don't think we can assume zombies could emulate that. So I don't think p-zombies could exist. But I don't think the Torah rules them out as much as straight logic does.