Absolutely.
As for your erroneous view that the ECFs didn’t consider the Church to be centered in Rone – guess again . . .
Clement of Rome
Accept our counsel and you will have nothing to regret. . . . If anyone disobeys the things which have been said by him [Jesus] through us, let them know that they will involve themselves in no small danger. We, however, shall be innocent of this sin and will pray with entreaty and supplication that the Creator of all may keep unharmed the number of his elect (Letter to the Corinthians 58:2, 59:1[A.D. 95]).
Ignatius of Antioch
You [the See of Rome] have envied no one, but others have you taught. I desire only that what you have enjoined in your instructions may remain in force (Epistle to the Romans 3:1 [A.D. 110]).
Irenaeus
But since it would be too long to enumerate in such a volume as this the succession of all the churches, we shall confound all those who, in whatever manner, whether through self-satisfaction or vainglory, or through blindness and wicked opinion, assemble other than where it is proper, by pointing out here the successions of the bishops of the greatest and most ancient church known to all, founded and organized at Rome by the two most glorious apostles, Peter and Paul, that church which has the tradition and the faith which comes down to us after having been announced to men by the apostles. With that church, because of its superior origin, all the churches must agree, that is, all the faithful in the whole world, and it is in her that the faithful everywhere have maintained the apostolic tradition (Against Heresies 3:3:2 [inter A.D. 180-190]).
Cyprian
With a false bishop appointed for themselves by heretics, they dare even to set sail and carry letters from schismatics and blasphemers to the Chair of Peter and to the principal church [at Rome], in which sacerdotal unity has its source" (Epistle to Cornelius [Bishop of Rome] 59:14 [A.D. 252]).
The Martyrs of Lyons
“And when a dissension arose about these said people [the Montanists], the brethren in Gaul once more . . . [sent letters] to the brethren in Asia and Phrygia and, moreover to Eleutherius, who was then [A.D. 175] bishop of the Romans, negotiating for the peace of the churches” (Eusebius, Church History 5:3:4 [A.D. 312])
Eusebius of Caesarea
Synods and assemblies of bishops were held on this account, and all, with one consent, through mutual correspondence drew up an ecclesiastical decree that the mystery of the resurrection of the Lord should be celebrated on no other but the Lord’s day and that we should observe the close of the paschal fast on this day only. . . . Thereupon [Pope] Victor, who presided over the church at Rome, immediately attempted to cut off from the community the parishes of all Asia [Minor], with the churches that agreed with them, as heterodox. And he wrote letters and declared all the brethren there wholly excommunicate. But this did not please all the bishops, and they besought him to consider the things of peace and of neighborly unity and love” (Church History 5:23:1–24:11).
Pope Julius I
“[The] judgment [concerning Athanasius] ought to have been made, not as it was, but according to the ecclesiastical canon. It behooved all of you to write us so that the justice of it might be seen as emanating from all. . . . Are you ignorant that the custom has been to write first to us and then for a just decision to be passed from this place [Rome]? If, then, any such suspicion rested upon the bishop there [Athanasius of Alexandria], notice of it ought to have been written to the church here
(Letter on Behalf of Athanasius [A.D. 341], in Athanasius, Apology Against the Arians 20–35).