No. That is incorrect
The Catechism:
“ the assembly of those whom God’s Word “convokes,” i.e., gathers together to form the People of God, and who themselves, nourished with the Body of Christ, become the Body of Christ.”
I say it again, The Church is the Body of Christ and it is composed of his believers. Not a brick building or a man made institution
Ephesians 5:23
For the husband is the head of the wife even as Christ is the head of the church, his body, and is himself its Savior.
1 Corinthians 12:12
For just as the body is one and has many members, and all the members of the body, though many, are one body, so it is with Christ.