This would be considered the legal union, correct? Then faith logically precedes vital union? What has priority between justification and vital union? I believe reformation theology has historically placed justification logically prior to vital union but that’s mainly from reading quotes from Reformers on Scott Clark’s blog.
In Reformation theology, it depends on who you read and in what context. The Westminster Standards present a specific logical order, but yes, you do see some diversity of opinions about the ordu salutis, though I have found in my own reading that union was emphasized more as prior to justification in the older writers, while those later are trying to guard the distinction between justification and sanctification, and make justification the basis for sanctification (often in an attempt to fight legalism or federal vision abuses). They would argue, like Berkhof does, that you can't have the transformative benefits (i.e. regeneration) prior to the forensic benefits (i.e. justification). But if so, then you have in a situation where faith precedes regeneration, or imputation/justification precedes faith (thus potentially opening a door to the idea of eternal justification, though Berkhof explicitly rejected it). But if you follow the Standards order, that Christ is acting as our federal head when he applies redemption to us, then that objection really goes away. Rather than receiving sanctification after justification, you receive them simultaneously through faith-union with Christ as dual benefits. The justification is not grounded upon the transformative grace, but upon Christ and his righteousness alone imputed through faith, while sanctification also begins through faith-union with Christ (Confession 14.2) at the same time. Note also another important nuance, that the Standards distinguish between regeneration and sanctification, but others make them synonymous (and so stress the need to keep justification prior). Again, it's a logical order, not chronological, since both sides of this discussion would agree it's applied instantaneously in time on the basis of Christ's prior headship and work.
So I would argue that yes, logically, faith precedes vital union, because it's through faith that we are united to Christ. Regeneration, faith, union, imputation, justification/adoption/sanctification, etc. Imputation happens automatically as a result of union with Christ and his righteousness. Christ is federally representing his elect as our surety (i.e. pactum salutis), prior to their actual possession of faith and justification, but they are not actually justified until faith receives Christ and his righteousness (Note Confession Ch. 11.4 on the timing of justification, "God did, from all eternity, decree to justify all the elect; and Christ did, in the fulness of time, die for their sins, and rise again for their justification: nevertheless, they are not justified, until the Holy Spirit doth, in due time, actually apply Christ unto them."). The concern to keep the forensic prior to the transformative is satisfied by Christ acting as our surety, not by the application of justification prior to sanctification. Through union with Christ, both are applied simultaneously.
The Larger Catechism 69-73 is helpful here too is stressing this order (effectual calling, regeneration, faith, union, imputation, justification)
69 What is the communion in grace which the members of the invisible church have with Christ?
A. The communion in grace which the members of the invisible church have with Christ, is their partaking of the virtue of his mediation, in their justification, adoption, sanctification, and whatever else, in this life, manifests their union with him.
70 What is justification?
A. Justification is an act of God's free grace unto sinners, in which he pardoneth all their sins, accepteth and accounteth their persons righteous in his sight; not for any thing wrought in them, or done by them, but only for the perfect obedience and full satisfaction of Christ, by God imputed to them, and received by faith alone.
71 How is justification an act of God's free grace?
A. Although Christ, by his obedience and death, did make a proper, real, and full satisfaction to God's justice in the behalf of them that are justified, yet in as much as God accepteth the satisfaction from a surety, which he might have demanded of them and did provide this surety, his own only Son, imputing his righteousness to them, and requiring nothing of them for their justification but faith, which also is his gift, their justification is to them of free grace.
72 What is justifying faith?
A. Justifying faith is a saving grace, wrought in the heart of a sinner by the Spirit and word of God, whereby he, being convinced of his sin and misery, and of the disability in himself and all other creatures to recover him out of his lost condition, not only assenteth to the truth of the promise of the gospel, but receiveth and resteth upon Christ and his righteousness, therein held forth, for pardon of sin, and for the accepting and accounting of his person righteous in the sight of God for salvation.
73 How doth faith justify a sinner in the sight of God?
A. Faith justifies a sinner in the sight of God, not because of those other graces which do always accompany it, or of good works that are the fruits of it, not as if the grace of faith, or any act thereof, were imputed to him for his justification; but only as it is an instrument by which he recieveth and applieth Christ and his righteousness.
We can see the same logical order in Belgic Confession 22, and Heidelberg Catechism 20, 21, 53, and 61 though not a clearly articulated as Westminster.
Sorry, didn't mean to write so much. Hope that is helpful... Again open to correction from others...