From what little I've read about him, I doubt he would have been able to turn the tide in the Cultural-Religious war for Rome. Though Christianity had yet to become a unified Church, and would more correctly be called the "Christianities" at this time since there was much infighting and dogmatic disagreements; nevertheless is was still profoundly more organized, centralized, and zealous than even the most die-hard of Pagan cults.

The war against the Christianities was an uphill battle from the start. Not only had Constantine I and his son Constantius II, the two previous Emperors who were the victorious "last men standing" in each of their respective civil wars, favored the faith and adopted it on their deathbeds; they even promoted it's expanse and financed the cult across the empire in an attempt to unify Rome through a new religion. It also didn't help that while Christian priests and laymen would rigorously help the poor, hungry, and downtrodden of society; many Pagan priests would spend so much time drinking, gambling, and whoring that Julian II himself would have to write letters to them reminding them of their sacred duties and how to do their job. The religious tolerance of Paganism, once a huge benefit to the Empire and it's path of easing the conquered peoples of Rome into Roman society by allowing them to retain their Gods, became a double-edged sword. While the Christians were extremely intolerant of other "false" Gods and worked day and night on converting and defining the faith, most Pagans really saw no need to extinguish what was in their minds, just another random God among many.

We should also look more as this being a battle of "states-of-divine-belief", rather than a contest between two "religions" in the modern sense. Paganism was more of a social contract; you negotiated with whatever Gods you wished and promised to honor them in exchange for good fortune to be bestowed upon you, your family, and the Empire. Failure to honor your side of the bargain would result in your ruin. Whereas Christians had a God who demanded nothing except "love for God and neighbor". Whereas the Roman Pagans worshiped in more "nationalistic" rites and had a worshiping mindset of competition and victory; Christians avoided this endless cycle of petty squabbles and perpetual competition between men and Gods by asking for a life of only love, community, and service. As with most aspects of human society, people get tired of the old rigid belief systems, and look for a new image that would distinguish their generation from the past. Already the traditional Roman Pantheon was looking stale and boring, so many Romans began adopting cults from the Eastern fringes of the empire; like Mithraism, the cult of Isis, the faith of Sol Invictus, and even the Christianities. Even the old Gods began to lose their old flavor; ie. Mars, the God of war, was replaced by Mithra and eventually Bellona. By the time the new cults came, it was a refreshing change of pace.

I think he prevented Christian schools from teaching the Hellenistic Classics by arguing that the philosophies and stories of ancient Greece were the religious property of Roman Paganism. Also he tried to use Christian tactics against the Churches by trying to design a religious system of Paganism, ie. Priests, Bishops, Parishes, etc.; that exactly mirrored the Christian version. From what I understand the policies were already slowly achieving their goals, isolate Christians to the fringes of society so far away from the sources of intellectual thought and power that they'd have to convert to avoid being lost in obscurity and irrelevance. If he didn't die in battle, Julian II may very well have turned the tide of the religious war; but personally I doubt it.

tl;dr Julian's law tactics of isolating Christians from anything relevant in society was working, however since he died at war we'll never know if he would have succeeded. Most likely not though since "out with the old, in with the new"