The Church is also typified as Bride of Christ, true, but neither in the very precise definition of the Church as the body of Christ, or in the bride typology will you find support for the Protestant doctrine of amorphous un-hierarchical “invisible church”. I can find plenty od scriptural support for the Church being visible, defined by baptism, hierarchical and sacramental structure.
No...no I looked in the mirror this morning and I'm not “invisible”. I've been sealed with the Holy Spirit as belonging to God.
Eph. 1:13,14, In Him, you also, after listening to the message of truth, the gospel of your salvation-- having also believed, you were sealed in Him with the Holy Spirit of promise,
who is given as a pledge of our inheritance, with a view to the redemption of God's own possession, to the praise of His glory.