With respect, I think the idea of a highly diverse early Church is overstated. If anything, what stands out is the remarkable uniformity of belief and practice across a culturally diverse Mediterranean basin. Too often contemporary scholarship (which has its own agendas) has latched onto marginal documents, such as the so-called Gospel of Judas, and inflated their import and authority with any real empirical warrant.
To take the cases of the heresies in question, none were really significant save for the qualified case of Donatism. Adoptionist theologies were arguably (I'd dispute the point) enunciated in some of the writings of Paul of Samosata and Theodotus of Byzantium, but there's little evidence that such views had wide adherence at any time; Adoptionism only became a significant issue in the Middle Ages, in 8th century Spain. Montanism had a brief, interesting life in central Anatolia but faded by the end of the 2nd century. Only Donatism posed a significant issue, and ironically, it only posed a problem once Constantine had legally allowed toleration for the Church - only then it did become apparent that there was a disagreement on how to treat those clergy and laity who had acceded to state demands under torture or imprisonment. Even so, Donatism has to be understood as more of a disciplinary issue than a doctrinal one, and it was spurred by the very state role we're debating here.
At any rate, it was a remarkably uniform Church which confronted Constantine in the 310's - not completely uniform, obviously, but certainly on questions of doctrine.
I'm not saying that there would have been no schisms down the road had there been no Constantine. I am saying that a) the Roman state was likely to reach some accommodation with Christianity, given its great extent in the most important parts of the Empire, and b) state recognition ironically provided an important precondition for the schisms we know eventually *did* take place in our own timeline.