You present an interesting hypothetical about Islam, the Koran, and the Bible.
However, you may have misunderstood the attitude of the Latter-day Saints toward the Bible. If I understand your post, you seem to imply that we view Momonism as "superseding" the Bible; that the Book of Mormon corrects the Bible; that Bible is "an inferior revelation"; and that few of us have any knowledge of the Bible. I do not believe those assertions to be true.
The Latter-day Saints consider the Bible to be scripture, just as we consider the Book of Mormon, the Doctrine and Covenants, and the Pearl of Great Price to be scripture. We also believe that God can, in his wisdom, reveal additional scripture. In other words, we have an open canon.
In my view, the Book of Mormon does not supersede the Bible so much as confirm it. Both books teach the Gospel of Jesus Christ. For this reason, both are vital to the Latter-day Saints.
Nor is the Bible "inferior" to our other books of scripture. The Bible is indispensable. It contains much that is not to be had in our other books of scripture, including the knowledge of the life and ministry of Jesus Christ and his apostles.
As for our knowledge of the Bible, I would point out that our Sunday School classes study the scriptures in a four-year cycle:
Old Testament (2006)
New Testament (2007)
Book of Mormon (2008)
Doctrine and Covenants, Pearl of Great Price (2009)
Note that this year's course of study is the Old Testament; next year's will be the New Testament. Thus, two years out of four our Sunday Schools study the Bible.
Now, I realize that some will say that Mormons read the Bible but do not understand it. I do not wish to start an argument with them about Biblical interpretation. That is a discussion for another day.
An ongoing revelation makes the Mormon religion a non-traditional religion. In any case, my perception is that In a NATION of Deseret, the on-going revelation would have taken a different direction. In a Christian country, more stress on the person of Jesus; in Deseret, less so. As you say, hypothetical, but what is not, is the severe reduction of Morman territory, in large part because of the issue of pologamy, ending in a threat to supress the whole Church. Then the new revelation that enables the Church to survive in a hostile society.