No, not yet.
Italian social media consultant Vincenzo Cosenza updated world map of social networks, and on this June 2012 version, Japan is painted in Facebook color.
I just refer my past articles.
- 2011: The year when Japan went global over social networking | The Japan Times Online
- Asiajin » Follow-up Of The Social Networking Column On The Japan Times
Why do English media keep repeating incorrect info on imaginary Facebook’s takeover? Because very few Mixi stakeholders exist outside of Japan, whilst there are people who earn more money if Facebook Japan being reported to reach the same level success as in US.
Twitter, which might have overtaken Mixi already (It is not possible to track Japanese feature phone web stats correctly.), may not want to advertise it much as they do not want to be seen as “popular but only in Japan” phenomenon when they are trying to chase Facebook popularity in US and the other regions.