This depends on how one might define Puritanism. In a sense, this poem can be read as a criticism of patriarchal society that has variously silenced and ignored the realities and stories of women for so long, and this could be seen as linking to a sense of Puritanism in the way that it silenced women and denied them agency. The speaker in this amazing poem starts off reading a book of myths to guide her to the wreck and its treasure beneath. However, at the end of the poem, having been transformed from her normal self into a new individual, a she and a he, the poem concludes with a realisation about that same book of myths:
a book of myths
our names do not appear.
The speaker realises, in her allegorical search of her subconscious, represented by the probing of the sea, that the book of myths, or literature and language itself, is something that has been dominated by males and is a patriarchal institution. This can be related to the Puritan forefathers of America and their views on women. The poem represents a challenge for women to tell their own stories and to make sure that their "myths" are now heard and recorded in history.