Neuroticism is more strongly associated with emotional stressors in the form of depression and anxiety than is extraversion. That being said, extraversion is negatively correlated with symptoms of depression, anxiety, and self-reported lifetime mental disorder, even after adjusting for gender, age, and education. It appears that depression is moderately linked to introversion in those who suffer from depression, whereas anxiety is not linked to introversion nor extroversion.
The results of this study indicate that:
It is argued that (a) one set of traits influences
positive affect or satisfaction, whereas a different set of traits influences
negative affect or dissatisfaction; (b) the former set of traits can be viewed as
components of extraversion, and the latter as components of neuroticism; and
(c) personality differences antedate and predict differences in happiness over
a period of 10 years, thus ruling out the rival hypothesis that temporary moods
or states account for the observed relations.
The paper further argues that one's happiness is relative to one's ability to adapt to new situations in healthy ways, which may be augmented in unhealthy ways by one's level of neuroticism.
So, to answer your question, it does appear that extraversion is linked to positive mental affect. However, it is worth noting that this does not necessarily imply that introversion is correlated to negative affect. It appears that neuroticism is a greater predictor of negative affect, which (hypothetically) could have a harsher impact on someone whose social support system is weaker or consists of fewer people, regardless of internal / external orientation.