Don Bradley concludes that the Alger/Smith relationship was Smith's first polygamous marriage.
Don Bradley, "Mormon Polygamy Before Nauvoo? The Relationship of Joseph Smith and Fanny Alger," in The Persistence of Polygamy: Joseph Smith and the Origins of Mormon Polygamy, ed. Newell G. Bringhurst and Craig L. Foster (Independence, MI: John Whitmer Books, 2010), 57
A polygamous marital relationship between Joseph Smith and Fanny Alger is better evidenced by the data than an extramarital affair, better fits the contemporaneous context, and holds greater explanatory power.
. . . .Though secret, atypical, and of uncertain officiator and date, Joseph Smith's relationship with Fanny Alger merits identification as his earliest known polygamous marriage.