Well, I do not believe that single persons can make huge difference in History. Changes derive from the general social needs and majority beliefs, although single persons in the correct position can accelerate things and provide some touch of their own in the developments.
Now, concerning Constantine, I think his contribution towards the legalization and final prevailance of Christianity was crucial, but overestimated due to later Christian accounts of his deeds. I guess his emmerge was the outcome of some party or clique within the Roman "court", and that's why he managed to change so many things in so little time.
So, if Constantine died early, I guess that this party should find someone else to fill his shoes, and although the process of the legalization and prevailance of the Christian Church would be delayed, the final outcome wouldn't be that different.
On the other hand, it is not definite that something identical to the Counsil of Nicea would happen. Even if Christianity would prevail as the major religion in the empire, I 'm not sure that, without Constantine, the Emperor would still become the head of the church and God's regent on Earth...