You said...
"The RCC came into existance in the 4th century with the uniting of Church and State under Constantine"
First of all ,The title Roman Catholic is actually the Diocese of Rome .
The Church has always been called Catholic
Here.....
How Did the Catholic Church Get Her Name?
by Kenneth D. Whitehead
http://www.ewtn.com/faith/teachings/churb3.htm excerpt
The term Roman Catholic is not used by the Church herself; it is a relatively modern term, and one, moreover, that is confined largely to the English language. The English-speaking bishops at the First Vatican Council in 1870, in fact, conducted a vigorous and successful campaign to insure that the term Roman Catholic was nowhere included in any of the Council's official documents about the Church herself, and the term was not included.
Similarly, nowhere in the 16 documents of the Second Vatican Council will you find the term Roman Catholic. Pope Paul VI signed all the documents of the Second Vatican Council as "I, Paul. Bishop of the Catholic Church." Simply that -- Catholic Church. There are references to the Roman curia, the Roman missal, the Roman rite, etc., but when the adjective Roman is applied to the Church herself, it refers to the Diocese of Rome!
Secondly,Constantine was an Arian,he was Baptized by an Arian Bishop,thus Constantine did not even believe in the divinity of Christ.
Constantine was responsible for the legalization of Christianity. Constantine was NOT the Founder of the Catholic Church.Jesus Christ is the founder of the Catholic Church
Lastly,
Here are some writings of the early Fathers of the Church-keep in mind that ST Polycarp and Saint Ignatius were DIRECT Disciple of the Apostle ST John.
"See that ye all follow the bishop, even as Christ Jesus does the Father, and the presbytery as ye would the apostles. Do ye also reverence the deacons, as those that carry out the appointment of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude also be; by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude also be; even as, wherever Jesus Christ is, there is the Catholic Church." Ignatius of Antioch, Epistle to the Smyrneans, 8:2 (c. A.D. 110).
"[A]ll the people wondered that there should be such a difference between the unbelievers and the elect, of whom this most admirable Polycarp was one, having in our own times been an apostolic and prophetic teacher, and bishop of the Catholic Church which is in Smyrna. For every word that went out of his mouth either has been or shall yet be accomplished." Martyrdom of Polycarp, 16:2 (A.D. 155).