I haven't done the birth certificate yet, but my court order specifically states that my gender is changed and that I am to be issued a new birth certificate.
When I went to the SSA to change my name there, my gender was changed too. Even though it's not listed on the card, it's in their records. Yeah, their web site seems to state that the gender can only be changed after surgery, but they changed mine because of the explicit text in my court order.