In a word, no:

Let’s look at the relationship between extraversion and leadership effectiveness.  Some studies have found a relationship, but it is so weak that it is difficult to draw conclusions from it.  A much stronger relationship has been found when looking only at particular types of jobs: extraversion predicts performance in jobs with a competitive social component; for example, sales.  And if we look at extraversion in more depth, it can also predict other less desirable outcomes such as absenteeism.

Introverts and ambiverts of the world, unite! There’s hope for you.

via HBR Blogs