The reason for Carly pulling out the “I’m female” theme is the answer to Hillary Clinton. Hillary is invested in making that theme the centerpiece of her own campaign focus, targeting women voters.
Carly is not doing the same for her health. She is taking it to Hillary and shoving it down her throat. (imho) :)
I believe you may be right, but in doing so, she has "stooped" a bit. IMHO, it would be better to simply tell folks that if they want to vote for a woman, do it because she's qualified and not because they find some allure with trailer park trash - wouldn't even have to mention Hillary and everyone would have no doubt of the target. It also puts Hillary in her rightful place.
Anyway, we could do worse than Carly, but we have a few better choices to try to boost before she becomes a real option.