Originally Posted by Dark Raven
Of course it makes sense. Hugh Laurie can speak in an American accent. He chooses not to when he's not playing House, because it's not his real accent. Same with the likes of Andrew Garfield or Henry Cavill, or conversely, Alexis Denisof and James Marsters who can sound like native Brits.
There's a difference between speaking your native tongue in the accent you learnt it in, and learning a new language in your own accent. The latter should be avoided (but is a lot of hard work).
When I had French evening classes recently, my teacher spent a lot of time trying to get me to lose my strong English language, because I am harder to understand to the French with a strong English accent. The more French my accent, the better I was speaking French.