Yes! Apparently they do! Up until recently finding this article, I believed that my American Toad, Shima, was a male because whenever it would rollover onto it's back, or when another toad would jump on it, or when I would pick it up.... it would chirp! So... I thought it must be a male BUT... as Shima grew larger, much larger than the other toads, and the throat appeared to be less shaded... actually there is no more shading, I now believe that He is a SHE!! Have a gander at the article... It's pretty good, especially for beginner's! Read under "Friends of Farmers and Gardeners"
https://mdc.mo.gov/conmag/2018-04/secret-life-toads