Agreed. She also would have been an excellent viewpoint character to see more of the European side of GW2. (Featherston could have sent her as his emissary to meet with the British and French throughout the conflict.)
In merely thinking that Colleton could be dispatched as an emissary, your own cultural blinders are showing. You're looking at the possibility as an inhabitant of the 21st Century decades after the women's rights movement has been active and not as the inhabitant of Turtledove's 1930s, socially conservative, alt-CSA.
While Turtledove's alt-USA is no beacon of sexual equality, there are women serving in Congress. Is there even a suggestion that a CSA counterpart to Flora Hamburger exists? Is there any hint of women holding elected positions at any level of CSA government? Or even serving in appointed positions other than prison guards?
A big part of Anne's POV is the comparison between the automatic racism/classism she inflicts on others and the automatic sexism others inflict on her. Politicians and political parties will take her money, but they won't really listen to her. She gets to chat with Wilson or Featherstone's minions because they're being polite and they want checks in the future. None of them are actually interested in her opinions or suggestions. She's just a pretty little thing who needs to be humored in return for contributions. She wants to be among the movers and shakers but they, because of her sex, only want to shake her down for money.
Look at the trouble Anne has making her own broker listen to her specific instructions with regards to her investments when the CSA's economy implodes after GW1. She has to directly threaten him with legal action and, if memory serves, remind him that her brother, a veteran of trench fighting, will call on him if her instructions are not followed. To her broker, Anne is incapable of making real decisions regarding her finances because she is a woman.
When you take time to remember the actual culture of the CSA Turtledove's series shows us, the idea that Anne Colleton or any other woman would be dispatched as an emissary or special ambassador is ludicrous.