The invisible Church are those who have faith in our Lord but one cannot discern who are a part of His invisible Church. However, Jesus and the disciples founded a visible Church and we see the formation of that Church in the book of Acts. This Church is the Catholic Church and is the self-same Church that Jesus prayed that we would all be one within. Otherwise as professed Christians and not being obedient to His Church would place us outside of His will, blessings, promises and grace; if not fully but in great measure. Those outside of His will would be those that some describe as "playing" at Christianity and not following Jesus.
There are some outside of the visible Church which some call a "remnant" that are not be on the path to the narrow gate but may be saved by God's mercy. These are those who seek God but are deceived into being outside of His visible Church by no fault of their own. While not a part of the visible Church they can be considered a part of the invisible Church. So, Jesus and the disciples formed a visible Church as we see after Pentecost recorded in the book of Acts and it could be said that there are those known only to God who are a part of that visible Church against their will or knowledge that will be received in Glory to be a part of the Church Triumphant. But, as one can see in Scripture this is not the ordinary way to be saved through His Church but as an extraordinary example of His mercy.
The gates of hell will never prevail against His visible Church because of the protection of the Church by the Holy Spirit given at Pentecost. The Church is other worldly and heavenly in its nature and is endowed with its holiness and veracity from its founder Jesus. Jesus gave His promises to His visible Church so that the world could see the testimony of His Church as the pillar and ground of the truth and a shining city on a hill (Mat 5:14) It is the will of God that all should be saved by and through His Church as it is the Church that was commissioned to spread the Gospel throughout the world both corporeally and individually. The Church is a refuge and the Ark from the sins and temptations of the world. It is heaven on earth where Christ dwells in the Tabernacles and is worshipped. So if the visible Church ceased to exist it would make Jesus a liar and a pretender as the Messiah and Savior of the world because all of His promises would be proven false.
Unity requires that there be a knowledge and physical manifestation of that unity. That is the Catholic Church which is the visible Church. The invisible Church does not represent unity because it is known only to God which may be unified in faith but not in purpose.
The purpose of the Church is its testimony in spreading the "good news" to the world. That requires a visible unity. The world will never know if those who are in the invisible Church are preserved but the visible Church will always be the witness to the world that it remains after empires and governments have fallen, political ideologies have been born and died and false and counterfeit religions have come and gone. It is a testimony that Jesus is God of the Trinity and that His will be done on earth as well as in heaven regardless of the snares of Satan and His lies against humanity.