I can see where the interpretation you ask about is plausible, however the progression in that text, Paul's practices of church discipline, and the precursor of Old Testament corporate punishment indicate that this "church" is more representative of the body as a whole rather than a metonym.
Jesus takes it from confronting with one person [v15] to confirming it (in obedience to the Law) by 2 or 3 witnesses [v16] to an even larger group in the church [v17].
But “if he does not listen,” that is, if he chooses to justify his sin
as if it were a just action, “take one or two others along with you,
that every word may be confirmed by the evidence of two or three
witnesses. If he refuses to listen to them, tell it to the church; and
if he refuses to listen even to the church, let him be to you as a
Gentile and a tax collector.” Don’t consider him now in the number
of your brothers. But not even so is his salvation to be neglected.
For even the heathen, that is, the Gentiles and pagans, we do not
consider in the number of our brothers, yet we constantly pray for
their salvation. - Augustine Sermon 82.7
Treating the sinner as a tax-gatherer or Gentile would be difficult for only leadership to carry out as the rest of the church (without being briefed on the circumstance) may wonder why he/she is being treated that way. For that person to not be numbered among the brothers, all the church would need to know.
Numerous times Paul calls out people in his letters: 1 Corinthians 5:1-13; 1 Timothy 1:20; 2 Timothy 1:15; 2 Timothy 2:17; & 2 Timothy 4:10,14. Those letters were sent to church leaders, but also circulated among the church as a whole. He tells the believers in those churches not to associate with those who have resisted correction. These instances appear to be a walking out of "telling the church".
In the Old Testament Law we find instruction on handling a sinner much the same way with accusation confirmed by investigation and witnesses then followed by all the people dealing with the sin.
If there is found in your midst, in any of your towns, which the
Lord your God is giving you, a man or a woman who does what is evil in
the sight of the Lord your God, by transgressing His covenant, and
has gone and served other gods and worshiped them, or the sun or the
moon or any of the heavenly host, which I have not commanded, and if
it is told you and you have heard of it, then you shall inquire
thoroughly. And behold, if it is true and the thing certain that this
detestable thing has been done in Israel, then you shall bring out
that man or that woman who has done this evil deed, to your gates,
that is, the man or the woman, and you shall stone them to death. On
the evidence of two witnesses or three witnesses, he who is to die
shall be put to death; he shall not be put to death on the evidence of
one witness. The hand of the witnesses shall be first against him to
put him to death, and afterward the hand of all the people. So you
shall purge the evil from your midst. - Deuteronomy 17:2-7
Obviously, Christ's instruction is not to stone them, but removing the obstinate from the church as a whole is consistent with the Israelite practices of sanctifying the community of faith.