While there are slight differences about which sentences exactly belong in the Bible and in which order, no (other) Christian Church has anything remotely like the Book of Mormon, and its existence is, from a purely theological point of view, a massive, huge, disqualifying heresy. You might almost as well consider Muslims to be Jews.
Culturally, of course, Mormons (more so than the Native American Church, which also references Jesus Christ. As does Islam, of course.) are part of the great American Protestant Christian Tradition. A somewhat divergent part, but clearly a part.
So bottomline. They're Christians, but not.