Lots of people have tried to write TLs about it, but it's a difficult task to do realistically because of a number of issues with Julian. People who try and do TLS based on Julian surviving have him creating a Neoplatonist utopia when for all the reasons that Basileus Giorgios goes over it would be a disaster. In addition is the fact that he was fighting the Sassanian Empire like they were the Parthians and he was doomed to fail because of it, even if he didn't die.
The problem with Julian is that he wasn't really being realistic about how the modern state worked, and the problems it faced. His plans to restore power to the civic councils, while admirable, would have totally destroyed the Diocletianic balanced budget that was needed to hold back the more formidable opponents of Rome that existed by the fourth century, while his Neoplatonism had much more in common with contemporary Christian ideas than it did with actual paganism as it existed on the ground.
I'm generally inclined to believe that a return to traditional style Roman paganism is impossible after the Third Century Crisis, simply because the old cults depended upon a way of life that could not exist after the middle of the third century. And once Constantius II had firmly consolidated Christianity's position as the leading faith of the Empire, I think it becomes very difficult for any serious alternative to Christianity to establish itself.
A surviving Julian would be a disaster as Emperor, and I'd be amazed if he were able to hold his throne for more than five years before being brought down by an armed revolt.
Americans: think of Julian as being a bit like Ron Paul. Intelligent, passionate, a fascinating figure: but ultimately not one with much connection to the real world.