I suppose that in the most purely theoretical sense it is possible. If you successfully gene edited an embryo so that it had an X chromosome in place of a Y chromosome, then you would have changed that embryo's sex. But then you've got a ship of Theseus situation where you'd have to ask if that embryo would develop into the same person, because you've modified its genes - would you still be you if someone had modified which copies of Chromosome 12 you had?
From a practical perspective once an embryo's developed physically the changes are kinda baked in. You could remove the extra chromosome 20 from someone with down's syndrome through gene therapy in theory, but they'd still have downs because they've already developed in a set way. Likewise with sex, by around day 30 the mesonephric duct is starting to differentiate into what will eventually become the cock and balls, or atrophying into the skene's gland and epoophoron.
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See how it says cloaca? That's how early in development this happens. Either way this is a bit like saying "in theory, since an animal's species is a physical reality, you can change a cat into a dog". In theory with enough gene editing you maybe could turn a cat embryo into a dog embryo, but it would probably spontaneously abort because - as always - biology isn't plug and play.
