If you live in one place for a period of time you might pick up some of the local accent,
I moved from Southern Germany to Austria a while ago. I now speak a weird kind of Standard German (intonation, wovel coloring, general accent) with Viennese words finding their way into my speech. I'd say my accent has become much more "neutral", though. My native dialect is Swabian, and I don't sound like that at all anymore, but whenever I'm home or meet another person from my area, my speech switches back within seconds. I'm always a bit surprised.
I guess the same would happen to an English speaker.