Yes, likely. But I don't think the top 10 in a unisex event under these rules would be all male.
I think these guys, and even those who are especially known for their flexibility, would have a hard time achieving level 4 laybacks and spiral sequences with +2 and +3 GOE, as the best female spinners and spiralers can achieve.
However, even without quads or an extra triple, they may still be able to make up enough difference in jumps to stay ahead.
Would expectations of carriage and body line still vary based on judges' knowledge of the skater's sex? If there were some way to make those aspects of Performance/Execution more standardized and the same for both sexes, it would be more of a disadvantage for Hanyu than it is in the men's event.
However, it's also something he can improve and that is much less dependent on body type than ability to rotate jumps or to pull ones foot over one's head.
I think it's a combination of biology and social expectations.
Male skaters under current rules have no need to train for extreme flexibility, so most of them don't. That's purely social.
I think on average women do have more flexible backs than men.
If male skaters did have strong incentives to train for maximum flexibility, we'd see a noticeably higher average level of flexibility among male skaters, and sometimes different skaters winning competitions. The more emphasis on flexibility and the less on jumps, the more difference we'd see on which male skaters win the medals and which are limited by body type in their potential to reach the top.
If a flexibility-based sport like rhythmic gymnastics were to become a male sport as well with the same rules and expectations as the female side, I would expect it would self-select for boys who, training from a young age, can achieve comparable levels of flexibility to the girls.
I also think that even with maximal flexibility training, the young men would start to lose enough of their flexibility by late teens (or sooner for those who reach physical maturity sooner) so that the older competitors would be at a disadvantage and the male sport would be dominated by 15/16-year-old boys. (Just as a version of figure skating that rewarded only jump rotation and not so much edge skills or presentation would be even more dominated by girls of that age than is already the case.)
However, for social reasons there is no sport that requires that level of extreme flexibility from male competitors. Artistic gymnastics even more than figure skating expects different skills from men than from women and therefore encourages male and female athletes to train their bodies in different ways and self-select out those who can't approach the ideal body type for their respective sports.
All skaters, regardless of sex, need to develop the best edge skills that they can. School figures as a separate discipline, for example, would have no need to divide competitions by sex.
The reason (don't shoot the messenger) that spirals and layback spins are traditionally regarded as "ladies" elements, is that ladies look so pretty doing them.
This is social expectations, but it's not a universal opinion. Although the general public -- especially the hegemonic heterosexual male decision makers -- may on average prefer to watch pretty ladies, there are plenty of straight female and gay male skating fans who prefer watching male skaters who make the effort to achieve pretty body positions over pretty ladies OR over men who focus only on athleticism/jumps.
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