EDIT: I'm rate-limited on comments, so if you come back here and read this, thank you for sharing from experience.
You will still have to deal with a ton of bureaucratic overhead and little moments where this is disclosed. For instance, your health insurance (and doctors) will usually know (the marker, not that you're trans, i get endometrial cancer screening recommended to me) and start to bicker about non-standard healthcare (i.e. I can get my estradiol tested at my GP, but for testosterone I need to see an endocrinologist) and your social security / employer will know (I also have at least 3 aliased social security numbers at this point).
Pure gender marker changes absent a name change are a lot less common, so it's not exactly well known territory.