That is a spurious argument. What you are saying is that prior to Constantine the Church was pure and apostolic when in fact since Apostolic times schisms and heresies abounded during the first few centuries after Christ. Couple that with the lack of communication and the savage persecutions which regularly occurred, it is not surprising that the Church in the 4th century was fragmented. Constantine unified the Churches under the authority of the Pope. 
Have you heard of the 'kairos' the opportune moment?  Then Constantine came upon the scene when God willed it.