Philosophical zombies by definition (See Chalmers: https://consc.net/zombies-on-the-web/) lack qualia, while being normal human beings in every other way. Like normal humans, zombies make utterances that appear to claim that they (zombies) have qualia.
If the inverted spectrum thought experiment makes sense for normal humans, does it still make sense when one replaces the normal humans with zombies? I don't mean inverted qualia, because, as Conifold has pointed out in a comment, a zombie has no qualia by definition, and therefore the answer would be of course, trivially, "no". But, according to Keith Frankish (https://twitter.com/keithfrankish/status/1659626995972489238?s=20 and https://twitter.com/keithfrankish/status/1659945605781700608?s=20 ) they might be visually inverted in other, functional ways, with one possibility being an inversion of affective responses to colors (see Dennett's fictional Mr. Clapgras in "Sweet Dreams" (here's a free pdf of the book, seemingly legal and free and safe, having been uploaded by Dennett himself: https://www.researchgate.net/profile/Daniel-Dennett/publication/329650273_Sweet_Dreams_Philosophical_Obstacles_to_a_Science_of_Consciousness/links/5d7a62ad299bf1ec8bd3573b/Sweet-Dreams-Philosophical-Obstacles-to-a-Science-of-Consciousness.pdf). Of course, such an inversion of emotional responses to colors would be experimentally detectable.
It is usual in discussions of zombies to ignore the possibility that normal humans lack qualia, since so few philosophers acknowledge that this is a real possibility with an appreciable chance of being the case. I am following this convention in this question but feel free to claim (as Dan Dennett does, for example in his book "Consciousness Explained" a free "precis", which is, in my humble opinion, actually more of a brief description of the book than a true precis of it, but is nevertheless worth reading, of which by Dennett can be read for free (at https://www.researchgate.net/publication/270356775_Consciousness_Explained/link/5f3d392d92851cd30203cdc1/download) and as Keith Frankish does in this video: "Lecture 1: The Illusionist Option" https://www.youtube.com/watch?v=Y2n-s6C1iYQ&list=PLhgvALi0LQGXIA7cKNmGNTiQ7dpS-7dLw) that we do lack qualia in your answer.