"Imagine you had a penis but otherwise felt exactly the same. Would you want to live as a man or would that not be OK? I would still feel like a woman and would consider myself a woman."
(1) You don't know that. If you had a penis you would also have testes and be running on testosterone. It is highly likely that you would want to live as a man.
(2) If I had a penis and associated biology, I would be a man. I would be born a boy, socialised as a boy, my entire life experience would be that of a boy and later of a man. Yes, I would consider myself a man, not least because anything else would be a delusion.