There was certainly offices (Bishops/Pastors/Elders/Deacons) but the organization consisted of local churches.
Now, in the 1st century of Christianity, before the completion of the New Testament, when churches would be established, it was the Apostles who were given responsibility of overseeing them.
The Council in Acts had to deal with the Gentiles being accepted as being equal with the Jews.
Remember even Peter and Barnabas had a problem with this later on (Gal.2).
The true church is made of only believers united by spiritual Baptism into the Body of Christ.
There are many visible churches, which contain both saved and unsaved people, Methodist, Baptist, Presbyterian, etc.
I think the bible reveals that the various churches were organizationally "connected" and that there were leaders occupying offices overseaing the churches and overseeing the elders within the churches.
I think we're going to disagree on this one, ftD. I've said my piece, though, and I respect you too much as a friend to enter any contest over it.