Isn't the idea of an "Invisible" Church basically a Protestant concept?
In a way, yes. Any community that claims itself separate from the Apostolic Church and yet is invisibly connected to the "Church of Christ" is invented. But I think there is a precedent where a person can unknowingly belong to the Church, the Apostolic Church. I think we can see this in the idea of re-baptism. Early in the Church History, about 250 AD, the Church decided that properly baptized men and women were considered Baptized, even if Baptized by heretics. So I think that there is something to be said about belonging to the Church of Christ, the Apostolic Church established by Him but not knowing it. We Latins call it "invincible ignorance". At what point this ignorance becomes obstinancy, only God knows.
Brother in Christ
The church is the body of believers, the body of Christ, whom God has called out from among men. As such it is an invisible church known only to God. The visible Churches consist of both believers and professors only.