The title question is sometimes asked of those who hold to Calvin/Turretin's view of Covenant Theology. I respond that the question seems to contain two flawed premises.
First, a mediator is a person who reconciles two parties. Christ does not serve as a mediator for the non-elect, only for the elect.
On the other hand, the non-elect members of the church should expect to receive something from Christ. It is written, "the Lord will judge his people." (Deuteronomy 32:36; Psalm 135:14; Hebrews 10:30) So, those who are merely outwardly part of the covenant should expect Christ to serve not as mediator, but as judge.
But Christ does not "mediate wrath" to those people, because that is not a mediatorial role. In his role as judge of all the Earth, Christ does not stand between God and man, but simply stands as God against man.
My emphasis on "outwardly," above, brings me to the second flawed premise. There are no non-elect members of the covenant of grace, under either the Mosaic administration or the NT administration. Those non-elect people who are part of the assembly/congregation/ekklesia but never believe are only outwardly members. Thus, they may bear the signs of the covenant (i.e. circumcision and/or baptism) but they lack the cleansing, forgiveness, and regeneration that those symbols represent.
The true Jew or true Christian is one who is one inwardly. Circumcision is of the heart.