Can the mystery of the Godhead be understood?

Yes.

The word “Godhead” is found 3 times in the KJV Bible (Acts 17:29; Romans 1:20; Colossians 2:9) and each passage uses a different Greek word ( theios, theiotēs, and theotēs ) for the same English word (Godhead). However, depending on the sentence structure, the word Godhead can have slightly different meanings.

“The”

Before The Word “Godhead”

When we ascribe this word “Godhead” to a being (individual entity) we affirm all that enters into the idea of God belongs to that being. When we say “the Godhead,” we are saying “God.”

(Act 17:29)

Forasmuch then as we are the offspring of God, we ought not to think that the Godhead ^(G2304) is like unto gold, or silver, or stone, graven by art and man’s device.

Forasmuch then as we are the offspring of God, we ought not to think that [God] is like unto gold, or silver, … 

But you should continue reading the rest of the passage

Act 17:30  And the times of this ignorance God winked at; but now commandeth all men every where to repent:

Act 17:31  Because he hath appointed a day, in the which he will judge the world in righteousness by that man [Jesus] whom he hath ordained; whereof he hath given assurance unto all men, in that he [God] hath raised him [Jesus] from the dead.

(Ref. Act 17:30-31)

(Col 2:9)

For in him dwelleth all the fulness of the Godhead ^(G2320) bodily.

For in him dwelleth all the fulness of [God] bodily.

Note 1:  However, in this passage the words “all” and “fullness” of God certainly do not mean the complete totality of God’s substance was all confined within the dimensional limitations of the human body of Christ, it is stated in the abstract. It is a  hyperbole.

Fulness, which is also an Ellipsis, signifies the full authority of God’s will and power that was manifest (revealed) to mankind through the body of Christ. (Eph 1:17, 22-23) (See Also: Act 17:30-31)

Eph 1:17  That the God of our Lord Jesus Christ, the Father of glory, may give unto you the spirit of wisdom and revelation in the knowledge of him:

Eph 1:22  And hath put all things under his feet, and gave him to be the head over all things to the church,

Eph 1:23  Which is his body, the fulness (full authority) of him that filleth all in all.

 and

(Act 10:38)  How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him.

(John 14:10) “I speak not of myself: but the father that dwelleth in me, he (God) doeth the works”

(2 Corinthians 5:19) “To wit that God was “in” Christ; < NOT > God was “incarnated as” the Christ.

Note 2:

This abstract type of language structure can be seen with other common phrases, “In Whom.”

(2 Peter 1:17) – “For he (Jesus) received from God the Father honor and glory, when there came such a voice to him from the excellent glory, This is my beloved Son, in whom I am well pleased.”

Even if you were to take “In whom” literally, this scripture clearly verifies several facts:

1.  God was not all in Jesus literally, for the voice came from heaven; (Mat3:17, Mark 1:11)

2.  God declared this man was his SON, not God himself speaking; and

3.  The Father is praising his son: “he received from God the Father honor and glory…”

To claim incarnation instantly destroys these TRUTHS.

There is not one scripture indicating that Jesus was a ventriloquist. This separate voice that came from heaven (the clouds in some translations) was God and God clearly stated what His relationship was (Father and Son). This voice did not say, this is my incarnated body of flesh in whom I am well pleased with myself, or I am pleased with myself.  There were witnesses to this event. Again, the phrase “in whom” did not mean the totality of God was all inside the body of Jesus literally, but that He (God) was pleased or proud of His Son. This was the ultimate “That’s my boy!” statement. (See also: In, In God, In Whom)

“And”

Before The Word “Godhead”

(Rom 1:20)

For the invisible things of him (God) from the creation of the world are clearly seen, being understood by the things that are made, even his (God) eternal power and Godhead ^(G2305); so that they are without excuse:

The closest meaning we have to describe the word “Godhead” in this passage (Rom 1:20) would be equivalent to the word “Godhood.” As manhood is that which makes a man a man, and childhood that which makes a child a child, Godhead is that which makes God God.

But He That Is Joined Unto The Lord Is One Spirit.

1Cor 6:17

1Co 6:17  But he that is joined unto the Lord is one spirit.

1Co 12:13 NASB For by one Spirit we were all baptized into one body, whether Jews or Greeks, whether slaves or free, and we were all made to drink of one Spirit.

Eph 2:18  For through him (Christ) we both have access by one Spirit unto the Father (God).

Eph 4:4  There is one body, and one Spirit, even as ye are called in one hope of your calling;

Php 1:27  Only let your conversation be as it becometh the gospel of Christ: that whether I come and see you, or else be absent, I may hear of your affairs, that ye stand fast in one spirit, with one mind striving together for the faith of the gospel;