There really is no "invisible Church" per sec. There is one Church, the Catholic Church, and all men are either members of it to some degree or not. Technically, there is no "Protestant Church". Those who follow the ways of Christ, but not baptized, are in some respects, part of the Catholic Church invisibly or to an unknown degree - but they are tied to a visible entity, even if unknowingly.
Those Protestants who have been baptized are to a larger degree (then say, a Muslim) in union with the One, Holy, Catholic and Apostolic Church - IF they do not reject His Church KNOWINGLY. For example, they read our Scriptures, believe many of our teachings (such as the Holy Spirit is God), they often practice our devotions, and so forth. In a sense, unknown to all but God, these persons are members of the visible Catholic Church. What we don't know is to what degree. We do know that only those who are full members of the Catholic Church ONLY possess the FULLNESS of the faith given by Christ. And God wills the salvation of everyone THROUGH the knowledge of the truth (and since the pillar and foundation IS the Church, so it is the vehicle for man coming to this full knowledge)
This does not mean that Protestants don't have "enough" of the faith. Only God can judge the complicity of their "heresy" or "disunity". "One cannot charge with sin of separation those who at present are born into these (Protestant) communities and in them are brought up in the faith of Christ" (Pope John Paul 2 in a homily at the Lutheran Church at Rome commemorating the 500th anniversary of the birth of Martin Luther). The Decree on Ecumenism points out that "these Churches (Orthodox) and ecclesial communities (Protestant), although defective (lacking fullness), have been by no means deprived of significance and importance in the mystery of slavation, but that they derive their efficacy from the Catholic Church (UR 3).
While it is true that the followers of other religions CAN receive divine grace, it is also certain that objectively speaking, they are in a gravely deficient situation in comparison with those who, fully within the Church, have the fullness of the means of salvation. Subjectively, of course, some Catholics have shown they do not desire the gift given to them, while other Protestants have made due with the limited gifts given to them. Thus, it is appropriate for Catholics to continue to evangelize, despite what some believe that the ecumenical movement does.
We are united by Baptism, but not by faith, and not by the one Loaf. Separation still exists, which is why we believe it is our duty to bring the full Gospel to our separated brothers - so that they may have the full knowledge of the Truth.
Brother in Christ
Since I know of the Roman Catholic church, and have not joined it, does that count as rejecting it knowingly?