We might have spirits based on old west legends and tall tales.
I think it'd be interesting if only because animism (which is one of the primary structural tropes that makes Gensokyo what it is) in the US has never been as pervasive an element in storytelling among all people groups the way Shintoism influenced so much Japanese thought, and that might have changed the way American!ZUN wrote Touhou Seihou. There are some people groups that do that more than others, though. You know who does? A lot of native American groups. See, for example, the concept of Wakan Tanka among the Sioux, and the whole Sun Dance idea among the Lakota.