Short answer
No. A "self-refuting" claim is one that involves explicitly contradictory logic steps, and that is not the case here.
Elaboration
What you are referencing is an empirical case:
- Our observations of the world come thru our consciousness, which is therefore apparently causally necessary to any further reasoning based on this data
- Our consciousness is not just central to our knowledge, but is also central to everything we do with it, as we consciously will our actions
- Physicalism is a model of our world that declares our consciousness to be at best secondary, a mere property of some other more fundamental reality, and non-causal. This generally is an assertion that consciousness is identical to some material structure, or that consciousness is not actually real at all.
- This appears to contradict the centrality of consciousness for 1 and 2.
Note for any data, the Quine-Duham Thesis notes that one can always find SOME tweak to a theory that makes it compatible with that data. Apply Quine-Duhem to materialism, and then SOME version of point 3 can present a rationale for why consciousness is only apparently, and not actually central to our lives.
The challenge for materialism from points 1 and 2 is different than this question presumes. It is not one of logical contradiction, this isn't a logic question. It is an empirical question, so the test should be an empirical one.
When we have direct empirical observations of the way things "seem", then for an alternative empirical theory that the way things "seem" is actually wrong, one generally needs two things:
- Significant evidence for the falsity of the apparent observation and for the truth of the alternative
- Predictive success for the alternative, showing for instance for an identity claim that A=B (consciousness = neurology) that whenever we have A, we also have B and whenever we have B, we also have A. Or for an illusion claim, wide recognition that the illusory nature of consciousness has been demonstrated in all cases.
The problem for materialists in general, and the reason that "the hard problem of consciousness" remains, is that while there are multitudes of postulated theories for what point 3 could be, none of them yet have passed either of the tests for empirical credibility. It remains far more reasonable to accept that consciousness is real, central, and causal.
Summary
The logical attack on materialism is wrong -- you can dismiss it by pointing out that this isn't a logic question, as Quine-Duhem will allow you to find some version of 3 that answers any logical rebuttal to materialism.
This answer does not help you as much as you hoped, because the NEXT question is -- how strong is the empirical case for materialism, and that brings one back the longstanding plausibility failure of all the point 3 answers vs. the Hard problem of consciousness.