I'm sure that someone with NC knowledge will be along presently. I'm in another state.
I assume that your DMV will accept a passport instead of a birth certificate. If you already have a passport with an F on it, you probably can't get a permanent change, and I don't know whether the temporary nature of the gender marker is supposed to be reflected on the actual passport. If you don't have a passport but wanted to get one, you would need a BC with the right sex on it.
My DMV cross-checks with the Social Security Administration. If I hadn't already changed my sex with SSA, I would not have been able to get the DMV sex marker changed.
What about a doctor's note? DMV requirements vary so widely...