My best friend would probably fall into this category. She's always doing more more more, and always excelling at all of it. But knowing her as well I do, I know she couldn't function any other way. I don't view her as an overachiever, but more as someone who thrives on chaos; she's someone who needs to be busy in order to stay sane.
I think this is true of many overachievers. They go crazy with downtime.