Maybe so, but the mainline Christians certainly didn’t understand things this way. The first Christian historian, Eusebius, for example, wrote an entire _History of the Church_ centered on the idea that the most important thing that ever happened was the conversion of the Emperor Constantine. He explored this idea further in two eulogies of the emperor, who has always been regarded in the eastern Church as a saint. I published an article on this topic in _The Greek Orthodox Theological Review_ about 15 years ago.
As far as Eusebius and his Orthodox successors were concerned, the Church was instituted by God, and St. Constantine’s role was to make Christianity the chief faith of the world — here understood as the Roman Empire. For Eusebius and his contemporaries, the sudden shift from persecuted faith to favored by the emperor could only have been worked by God. It received its astounding validation when Constantine attended the Synod of Nicea and touched the wounds of confessor-saint bishops and monks in attendance. Imagine, an emperor formerly leader of a state religion that worshiped worldly power and beauty supporting the carpenter-God’s Church and embracing its disfigured leaders. This was breath-taking.
You can see the legacy of Eusebius’s understanding in the testament of Vladimir Monomach, for example. The Russian Primary Chronicle is chock-full of stories of rulers embracing and following this model.