I actually tend to be an introvert -though am very friendy, if that seems like a dichotomy- and a bit socially anxious, and yet when I'm hypomanic, all of that melts away. Or rather, flies away in a big, earthshattering burst.
I lose all social anxiety, I become very much an extrovert, I think I'm the most brilliant person in the world -and let others knows it, in some way or another- am hyperactive (including little needed sleep), hypersexual... I do a 360, I completely change.
Though when it turns to mania, the hyperactivity turns into the unbearable need to move and as if bugs were crawling all over me, the extroversion and hypersexuality turns dangerous, the delusions start to take me over.
So, to answer your question, no, I don't turn inward, I actually very much turn outward.