Sure. Accents aren't hereditary. We learn to speak a language by listening to others and imitating their speech. Within a language, accents are often regional because the people in that region learned by imitating those around them. If you can imitate a different accent and do it long enough, it will become your natural speech.
I did. Two medical anthropologists and a speech pathologist I met by chance about 2 years after the switch told me that the degree to which I changed was rare and difficult... that they wouldn't have known if I hadn't mentioned it. I'm not really sure how I did it. It felt like a natural change and it feels completely natural now. I don't even revert when I'm upset or sleepy.