I think the short answer to your question is “yes,” although I am not sure I understand your use of the word “justified.” The word seems to suggest a question of “worth,” as in, “What’s so special about Walt? Why does he deserve a poem about himself?” It’s a good question, but one that misses the point of "Song of Myself."

Whitman's purpose in "Song" is to eradicate the difference between subject and object. That is to say, there is no difference, in his view, between himself and other people. He is very explicit about this from the start of the poem. When he says, in the third line, “For every atom belonging to me as good belongs to you,” he’s not being symbolic or mysterious: he is positing the commonality of all people. I think the poem is an attempt to use his life as a kind of gateway to this shared (“democratic,” he would say) experience.

This requires a kind of radical openness to new experiences, and, in my opinion, a redefinition of “self.” The “Myself” Whitman celebrates is not the same as Walt Whitman the man, although it includes that person. He is, as he says in section 4, “Both in and out of the game and watching and wondering at it”—both participant and observer. In this way, the poem perhaps could just as easily have been called “Song of Ourselves.” In this sense, the question of “justification” really doesn’t apply. As Whitman says, “I have no mockings or arguments, I witness and wait.”

Whitman's contribution to poetry was not only stylistic--eschewing rhyme and meter--but personal as well. Rather than hiding behind a first-person personal narrator a la the Romantics, or disguising his message in an extended narrative a la the Fireside poets, he chose to give himself, to "sing" himself,his individuality. In a free autobiographical voice, he celebrates his (and, by extension, our) uniqueness, part of the natural universe, not categorized or taxonomized, an individual soul.   His love of the present moment, his joyous affinity with nature, his "song of himself" is worth celebrating.  This kind of declaration of selfhood is virtually unique in literary history.