Not now. I've had British people describe my accent as "the softest American accent I've ever heard", pretty much neutral Californian.

Now when I was a kid I lived in the deep South and had the most deep fried Southern drawl you can imagine. I moved to California when I was in middle school. My Southern accent was gone inside a month. The funny thing is that while I don't speak with one anymore, I can still understand it as well as ever. Once I was in a restaurant with my wife and daughter and a woman with an overpowering twangy accent asked directions to a local ice cream joint. They looked at her like she was speaking Klingon. I just calmly gave her directions.