Before we begin to study the purpose of the Order of Melchizedek let us be perfectly clear.  We can no more assume or attain a place in this order by our own strength than we can leap to the moon in a single bound.  This is entirely a work of the Holy Spirit in each of us individually.  As Hebrews says,

For every high priest chosen from among men is appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for sins.  [2] He can deal gently with the ignorant and wayward, since he himself is beset with weakness.  [3] Because of this he is obligated to offer sacrifice for his own sins just as he does for those of the people.  [4] And no one takes this honor for himself, but only when called by God, just as Aaron was.
    [5] So also Christ did not exalt himself to be made a high priest, but was appointed by him who said to him,
    “You are my Son,
        today I have begotten you“… Hebrews 5:1-5 (ESV) 

Yes, the one who becomes part of the Order of Melchizedek can only be one of the “manifested sons,” one of the remnant overcomers who is glorified and given a new body at what we commonly call the rapture.  Men err greatly when they teach that all Christians partake of the parousia.  Many will be disappointed that day for only the elect (those people now called the saved) will participate.  Let us hope and pray that we will be chosen.  Remember, in our flesh dwells no good thing.  We grump and we sin daily.  But, let us repent continually; let us practice righteousness so that when He comes we may be accounted righteous and holy before Him and may see His face. 

Peter explains the purpose of God’s holy priesthood:

As you come to him, a living stone rejected by men but in the sight of God chosen and precious,  [5] you yourselves like living stones are being built up as a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ.  [6] For it stands in Scripture:
    “Behold, I am laying in Zion a stone,
        a cornerstone chosen and precious,
    and whoever believes in him will not be put to shame.”
 [7] So the honor is for you who believe, but for those who do not believe,
    “The stone that the builders rejected
        has become the cornerstone,”
     [8] and  “A stone of stumbling,
        and a rock of offense.”  They stumble because they disobey the word, as they were destined to do. [9] But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light.  [10] Once you were not a people, but now you are God’s people; once you had not received mercy, but now you have received mercy.
    [11] Beloved, I urge you as sojourners and exiles to abstain from the passions of the flesh, which wage war against your soul.  [12] Keep your conduct among the Gentiles honorable, so that when they speak against you as evil doers, they may see your good deeds and glorify God on the day of visitation.  1 Peter 2:4-12 (ESV)

Priests in the Order of Melchizedek  proclaim the excellencies of him who called them out of darkness into his marvelous light.  These priests are ambassadors of Christ who will rule the world with Christ’s rod of iron in the age to come, the great millennial reign of Christ.  Then will be fulfilled that word of Paul’s, 

“the mystery hidden for ages and generations but now revealed to his saints.  [27] To them God chose to make known how great among the Gentiles are the riches of the glory of this mystery, which is Christ in you, the hope of glory.  [28] Him we proclaim, warning everyone and teaching everyone with all wisdom, that we may present everyone mature in Christ.  [29] For this I toil, struggling with all his energy that he powerfully works within me.  Col. 1:26-29 (ESV) 

At this time, and not until then, 

The earth will be filled
        with the knowledge of the glory of the Lord
        as the waters cover the sea.  Habakkuk 2:14 (ESV) 

And it will be those priests in the Order of Melchizedek who bring this knowledge to the whole world, yes, to every man.