Speaking with a native accent is not so important to communicate in the foreign language. However, it is very important to have a good pronunciation. Here is a video of Rafa Nadal's interview at the Roland Garros tournament. As you can see, Rafa is using a correct English, but with a Spanish accent.
http://www.youtube.com/watch?v=EYL_7xTSFE8&feature=PlayList&p=0E93ADA420FC1DF5&playnext_from=PL&playnext=1&index=39
