Yes, those who confess Jesus as their Lord make up the true church, and this body of believers will be evident as believers; you cannot be an incognito Christian; if you are true, there will come a moment when someone asks you why you are different and you will be called upon to either confess or deny Christ as the reason why you are different.
What we mean by the church being an invisible body is that there may be some who claim to be in the church who do not have a living and saving faith in Jesus Christ. These may be in the church "visibly", that is, they appear to be Christians because that is their profession; but "invisibly" that is, behind the scenes, they are not Christians at all, because they don't really believe.
People claim to be Christians when they are really not for a variety of reasons. I think that the primary reason is that they feel that if they say they are a Christian, people will not attempt to convert them to Christianity. So they say they are Christians to get people off their backs. Some others, feel that there is a certain prestige in being called a Christian, because of the moral superiority of the faith to other religions. Also, there is jailhouse Christianity. And there may be other reasons also.
The point being that there are those who claim to be in Christ who are not really saved. And these are "visibly" in the church, but not "invisibly".
So, with the Catholic Church, the majority of them may be visibly in the church as an organization; but unless they have a living and saving faith in Jesus, they are Christians in name only and are not a part of the true church. In other words, religion doesn't cut it to identify you as a true Christian.
