How would they take it?

There's been a lot of female Yang posts these days. This has made me wonder something.

What if the Yang child was a girl instead of boy. Her life story follows the original's pattern: father dies, goes to the Academy, El Facil, Econia all the way to Tiamat and Astarte.

I wonder how Reinhard and his admirals, whose society is more patriarchal than the Alliance (Kircheis at one point says that women in the Alliance fight in its military, meaning they don't in the Empire), deal with the fact that the Alliance admiral who is giving them the most trouble is a woman? Would there be significant changes in how they'd react to Yang's ability to counter them on the battlefield?