Yes. And unlike most of the other charges, no philological remark helps here: the passage stands in the main text, it comes from Hegel, and it says what it says.
What stands there
In § 166 Hegel distributes the spheres: the man has „his actual substantial life in the state, in science, and the like“, the woman has „her substantial determination“ in the family. In the note the Antigone becomes the proof: piety as „the law of woman“, against the manifest law of the state. The Addition goes further still and compares women’s education unfavourably with men’s.
With this half of humanity is excluded from what the book develops as the highest shape of freedom. This is no marginal sentence. It is a building block: the separation of family and civil society acquires its sharpness in Hegel precisely because the two spheres are staffed by persons.
The real point at issue
It is not whether Hegel is wrong here – nobody disputes that – but whether the error can be removed without damaging the system. Two answers stand against one another.
A judgement of its time. Hegel writes in 1820, and what he says about women is the convention of his age, not the result of his concepts. Strike it, and the architecture still stands: nothing in the determination of the family as immediate ethical life requires that it be the woman who is absorbed in it.
Necessary to the system. The feminist criticism – Carole Pateman, Seyla Benhabib – replies that the exclusion is needed. If the family is to remain a sphere with a right of its own and not to dissolve into civil society, someone has to live wholly within it; and the mediation between the spheres works only if they are unequally staffed. Whoever strikes the exclusion has to explain how the family is then anything other than a contract between private persons – which Hegel expressly denies (§ 75).
What can be said with Hegel against Hegel
The strongest counter-argument is supplied by his own text. In the note to § 209 stands: „The human being counts, thus, because he is a human being, not because he is a Jew, Catholic, Protestant, German, Italian, and so on.“ The series is open; it names marks that contribute nothing to counting as a person. Whoever takes this sentence seriously cannot exempt sex – and Hegel gives no ground for doing so that would come from the concept, only a description of what he saw before him.
It is the same figure as at other points where Hegel goes astray: a found shape of actuality is taken for the actualisation of its concept, without the examination being carried out. That is the standing risk of his procedure.
Sources. § 158 to § 181, especially § 166 · Carole Pateman, The Sexual Contract, 1988 · Seyla Benhabib, „On Hegel, Women and Irony“, 1991 · Patricia Jagentowicz Mills (ed.), Feminist Interpretations of G. W. F. Hegel, 1996. – On this website: The feminist criticism.