Sure, "As I Ebb'd" is doing its own thing, form-wise. Still, even the most non-traditional poems still have a sound. After all, free verse doesn't mean free of poetic devices. Every good poem has a few of these up its sleeve.
For example, try reading the following aloud:
As I wend to the shores I know not,
As I list to the dirge, the voices of men and women wreck'd,
As I inhale the impalpable breezes that set in upon me, (18-20)
Notice anything? All three lines begin with "As I [verb]." Viola—that's anaphora at work, the repetition of words or phrases at the beginning of a line.
Typically, Whitman uses anaphora when he wants to emphasize something. Here, in the beginning of Part Two, he wants us to really emphasize that the speaker is behaving repetitively, just as the ocean does with its constant coming-and-going of the tides.
And that's not all; Whitman has other sonic tricks that remind us of the sea. He frequently uses alliteration, or the repetition of initial consonant sounds. For example:
Up just as much out of fathomless workings fermented and thrown, (66)
"Fathomless" and "fermented" create a repetitive echo with these repeating F sounds, creating a sense a bit like being on a ship, rocking back and forth. And that's not the only thing going on in these lines. The W sound is repeated in both "workings" and "thrown." This trick is called consonance.
Sonic elements like these really add to the cadence of the poem, but they do more than that. If you've ever stood on a beach, you know that the sound of the waves is an important part of the experience. By packing these lines with echoes, Whitman subtly underscores his speaker's sonic sensations. It turns out that he had more up his sleeve that it might initially seem.