Do you think that following Emerson's philosophy, as described in "Self-Reliance," would lead to happiness?
I think you can defend at least two different answers to this question.
First, you can reasonably argue that a follower of Emerson's philosophy would experience a particular type of happiness called "eudaimonia." This isn't the kind of happiness that makes you laugh, but rather the type that makes you feel your life has meaning.
Second, you might argue that the ultimate goal of this philosophy isn't any sort of happiness—not even the eudaimonic type. Instead, the goal is to transcend all normal human emotion and replace it with a godlike appreciation for what's right and true about the world.
Let's take each answer in more detail.
Psychologists recognize two different kinds of happiness. Hedonic happiness is what we feel when we gratify our senses, seek pleasures, and avoid pain. Eudaimonic happiness is the reward we find meaning in life, experience a sense of purpose, or perceive ourselves to be learning, improving, or realizing our potential. Eudaimonic happiness has been linked with both a sense of autonomy —striving towards personal values or goals—and a sense a meaningful, social connectedness.
Clearly, Emerson warns against expecting a lot of hedonic happiness. We might experience some, because Emerson is telling us to follow our best impulses, and these impulses may lead to pleasurable sensory experiences, like listening to music. If we march to our own drum, though, other people will oppose and misjudge us. Life will be more difficult:
For nonconformity the world whips you with its displeasure.
Eudaimonic happiness is a different matter. Emerson speaks of the sense of satisfaction that comes from doing what you are intrinsically motivated to do:
A man is relieved and gay when he has put his heart into his work and done his best.
Emerson hints that adopting his philosophy delivers peace of mind:
[T]he great man is he who in the midst of the crowd keeps with perfect sweetness the independence of solitude.
There is the obvious point: Following your inner voice may mean doing what you love.
I will so trust that what is deep is holy, that I will do strongly before the sun and moon whatever inly rejoices me, and the heart appoints.
Presumably, Emerson is talking about more than purely hedonic pursuits here. Throughout the essay, he cites the work of philosophers, artists, and scientists who produced great intellectual work, and Emerson himself was a poet. Doing what "inly rejoices him" includes activities that bring a sense of meaning and self-improvement.
Yet we could also argue that the ultimate aim of Emerson's philosophy isn't any sort of happiness—at least, not as we usually define the term. Emerson thinks the ultimate goal is transcendental, to rise above one's self. This involves leaving our normal passions behind.
In the hour of vision, there is nothing that can be called gratitude, nor properly joy. The soul raised over passion beholds identity and eternal causation, perceives the self-existence of Truth and Right, and calms itself with knowing that all things go well.
Taking on this "God's eye view" of the world means transcending the private self and our personal emotions. In that respect, the true Emersonian might not have feelings that match the definition of eudaimonic happiness, but he or she will feel this timeless, calm sense that "all things go well."
Ryan RM and Deci EL. 2001. On happiness and human potentials: a review of research on hedonic and eudaimonic well-being. Annu Rev Psychol. 52:141-66.