According to Latter-day Saints, are all Christians who are full of the Holy Spirit unequivocally led by the Spirit to accept the truth of Mormonism?

I see at least two possible interpretations of the word "fullness" here. One is a temporary fullness, which is a term used to describe what was felt by many who experienced a manifestation of the Holy Ghost. However, having such an experience does not entail a permanent change or lasting fullness. So the greater fullness must be continuous rather than temporary, which requires reception of the gift of the Holy Ghost, which is not only the principle of revelation, but is also the promise of eternal life. A person cannot be completely "filled" without this ongoing assurance from the Lord or without continued experiences safeguarded by covenants and faithfulness.

It is not possible to experience ongoing fullness of the Holy Ghost (which implies His constant companionship) without first being baptized and confirmed a member of the Church of Jesus Christ of Latter-day Saints. So yes, everyone who meets that description (a Christian continually full of the Holy Ghost) has to have been converted to the Savior's true Church and received this gift by the one authorized by God to administer it.

A person may have experiences with the Holy Ghost before he is baptized, and the effect of these experiences is to lead him to the truth, so that he desires to be baptized and confirmed so as to be able to enjoy His presence as a gift in perpetuity:

"Cornelius received the Holy Ghost before he was baptized, which was the convincing power of God unto him of the truth of the Gospel, but he could not receive the gift of the Holy Ghost until after he was baptized. Had he not taken this sign or ordinance upon him, the Holy Ghost which convinced him of the truth of God, would have left him." Joseph Smith Jr.

Can a transient experience with the Holy Ghost be termed a "fullness"? If so, it is not the fullest fullness, and so cannot be the fullness spoken of by Scripture, whereby a man is saved.

is it possible to be a Christian full of the Holy Spirit and simultaneously not be led by the Spirit to accept the Book of Mormon as divine revelation?

Ultimately, no. To reject the testimonies of The Book of Mormon is one and the same as rejecting Jesus, Whose words they are.

I agree with Hold to the Rod's opinion,

is it possible to be a Christian full of the Holy Spirit and simultaneously not be led by the Spirit to accept the Book of Mormon as divine revelation?

My personal opinion is:

Temporarily - yes

Permanently - no

I wanted to offer some scriptural evidence for why the "Temporarily - yes" portion of the answer holds.

Scriptures

Joseph Smith taught that there are honest seekers of truth (I don't know if that's an exact parallel for having a fullness of the Holy Ghost) who do not find the truth,

For there are many yet on the earth among all sects, parties, and denominations, who are blinded by the subtle craftiness of men, whereby they lie in wait to deceive, and who are only kept from the truth because they know not where to find it. (Doctrine & Covenants 123:12)

Again, I don't know if the "pure in heart" this is specifically in reference to (see verse 11) match what the OP is asking about, those with a fullness of the Holy Ghost, but the teaching is there that there are those who would presumably seize upon the truth if they know where to find it, and if they weren't "blinded by the subtle craftiness of men."

Joseph Smith also taught,

Thus came the voice of the Lord unto me, saying: All who have died without a knowledge of this gospel, who would have received it if they had been permitted to tarry, shall be heirs of the celestial kingdom of God;

Also all that shall die henceforth without a knowledge of it, who would have received it with all their hearts, shall be heirs of that kingdom; (Doctrine & Covenants 137:7-8)

There is the strong implication in these verses that there are those who would receive the truth who, for whatever reason, are kept from it or do not find it while they are alive.

Additionally, Latter-day Saint teachings speak of the "spirit world," a place where our spirits dwell between death and the resurrection, where the gospel is taught to those who have not yet received it. This is taught throughout Doctrine & Covenants Section 138. The existence of missionary work among the dead, as well as the proxy ordinances of salvation (such as baptism) performed by living Latter-day Saints in temples, bear powerful testimony of the belief that there are many among the dead who have not yet received the gospel as taught and practiced by Latter-day Saints but either have after they died or will yet after they die.

Why

This brings up the question, why would God not provide opportunity for some seekers of truth to find the Book of Mormon and restored fullness of the gospel? I'm sure there are many reasons not know to us, but one that occurs to me is that life is a personal classroom for each one of us. God knows what we need to experience to help us achieve maximum happiness in the eternities, and as different as we all are, each of our needed life experiences are also vastly different. Since He has provided a way for people to learn and receive the fullness of the gospel after they had died, if a needed life experience for a person does not involve them knowing the fullness of the gospel yet, He can provide that and still have their eventual learning of the fullness of the gospel covered. This last bit is speculation by me, in that I don't know if I have ever actually seen in taught in official Latter-day Saint sources.

Yes if one is full of the Holy Spirit they will be led to the truth of the Church of Jesus Christ (if they have knowledge of it). Others can of course be touched by the Holy Spirit or be inspired.

The promise shared at the end of the Book of Mormon in Moroni 10:4 specifies

4 And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost.

As further explanation Elder Anderson¹ says:

President Dallin H. Oaks visited our mission in Bordeaux, France, in 1991. He explained to our missionaries that real intent means that the person praying is saying to the Lord something like this: “I do not ask out of curiosity but with total sincerity to act on the answer to my prayer. If Thou wilt give me this answer, I will act to change my life. I will respond.”

Please note the LDS also believe:

All honest seekers of the truth can feel the influence of the Holy Ghost, leading them to Jesus Christ and His gospel.²

Or put another way:

I quoted Doctrine and Covenants 130:20–21: “There is a law, irrevocably decreed in heaven before the foundations of this world, upon which all blessings are predicated—

“And when we obtain any blessing from God, it is by obedience to that law upon which it is predicated.”

I then told him that “if anyone obeys any eternal principle he will automatically reap the reward for living that law. God will give any and all men his or their reward.” We as Latter-day Saints do indeed believe that there is truth in many religions and philosophies. Many good and great religious leaders have walked the earth. Through their teachings, they have raised the spiritual, moral, and ethical awareness of their people.

When we speak of The Church of Jesus Christ of Latter-day Saints as the only true church, we mean that it is the only organization authorized to administer the ordinances of salvation. We mean that it is the only organization led by Jesus Christ, through the earthly ministries of prophets and Apostles. Although the Church teaches the true doctrines of salvation, we do not mean that it is the only teacher of truth.³

_{1 Spiritually Defining Memories footnote 19}

_{2 Holy Ghost}

_{3 What is the relationship of the church of Jesus Christ of Latter-day Saints to the non Christian Religions of the World}

_{See also Living with Purpose: The Importance of Real Intent}