Supposedly during Tang Dynasty, two Chinese Nestorian Christian Monks, seeing the inconsistencies and incompleteness of their holy texts (which was a real problem if you read Nestorian inscriptions), and inspired by Xuanzang's pilgrimage to India, set out and traveled to the (Eastern) Roman Empire, called "Fulin" in Nestorian texts.
And because the Byzantine version of Christianity was much more developed, with their ceremonies, canons and all, the two monks were fully engulfed by it. They eagerly learned, and bought into the Roman version whenever it contradicted their previous believes, considering them their own "mistakes".
The Chinese monks, after decades of study and great theological achievements, returned to the Tang Empire with camel-loads of Christian canons and a fully developed theological system in their head. They dedicated rest of their lives to translating the Greek texts they brought back from the Roman Empire, and their church attracted a large following with full imperial blessings.
If the story seems implausible, you can ignore it or change the story. But let's assume Eastern Orthodox Christianity in its fully developed form did really take root in China.
What, then, would be its impact on Tang history and, it it survives, subsequent Chinese history?