Success is counted sweetest
By those who ne'er succeed.
To comprehend a nectar
Requires sorest need.
The speaker in the poem says that those who never succeed actually understand success the best. The defeated person understands success more fully than the victor in war (purple host as the army or nobility) or in life. One of the characteristics of transcendentalism is self-reliance or self-wisdom; the idea that all humans have innate wisdom and can achieve profound knowledge by themselves. For instance, a transcendentalist would achieve a connection to God without the mediation of a religious institution.
In this poem, the defeated person understands (or appreciates) success more than the victor. This suggests that the defeated person comes to this knowledge, not by experiencing success, but by intuiting success by himself. He intuits success, achieves this self-wisdom without the social experience of success. Consider this analogy that a person understands and appreciates water much more when she is thirsty than when her thirst is quenched.
The defeated person is therefore most sensitive ("sorest") to the sweetest parts of life (nectar and success) and he is therefore in tune with the nature of his feelings, aspirations, and desires. Recognizing the connection between the soul and nature is a transcendental aspiration. To "comprehend a nectar," to fully understand the sweetness of nature, one must be mentally and physically sensitive to nature. So, yes, you could argue that the defeated person understands success better than the victor who has experienced a success in the eyes of society. Thus, the defeated person has transcended social success and understood it on a personal, perhaps more profound, level.