First, you should be aware that not all of Mormon doctrine, or even of the things that are generally considered "the stuff that makes Mormons unique among Christianity," is contained in the Book of Mormon. A lot of it is found in the Doctrine and Covenants, a compilation of revelations and historical context from the early days of the modern-day church.
Having said that, the answer is yes. 2 Nephi chapter 28 describes the latter days, before the coming forth of the Book of Mormon and the restoration of the the church, as a time of universal apostasy, when "the churches which are built up, and not unto the Lord, when the one shall say unto the other: Behold, I, I am the Lord’s; and the others shall say: I, I am the Lord’s; and thus shall every one say that hath built up churches, and not unto the Lord," and states "Yea, they have all gone out of the way; they have become corrupted."
Likewise, Mormon chapter 8 speaks of the same time period as a time of corrupted and apostate churches.
Also, even if such prophecies were not contained in the Book of Mormon, it seems that acceptance of the book implicitly requires acceptance of the concept of the Great Apostasy:
- To accept the Book of Mormon necessarily requires accepting its origin: that it is an ancient record that was found and miraculously translated--by a farm boy with very little formal education--through the power of God.
- To accept this requires accepting that Joseph Smith was called of God as a prophet, given the power to translate the record, and shown where it was located.
- To accept this requires accepting his story of what happened, including the part where, when Joseph prayed to God to know which of the many churches of his day was the correct one that he should join,
19 I was answered that I must join none of them, for they were all wrong; and the Personage who addressed me said that all their creeds were an abomination in his sight; that those professors were all corrupt; that: “they draw near to me with their lips, but their hearts are far from me, they teach for doctrines the commandments of men, having a form of godliness, but they deny the power thereof.”
Therefore, accepting the Book of Mormon necessarily implies accepting the Great Apostasy.