The Great Awakening contributed somewhat to the development of the idea of a separation of church and state. Mainly, it did this because it contributed to the development of many different sects of Protestantism within the colonies.
At the time, most colonies had official, established religions. These were supported with tax money. The Great Awakening brought new challenges to these established churches. Splits occurred in the old churches, with some members even joining new sects that were in favor of the ideas of the Great Awakening. As more people came to identify with these other, non-established sects, they were inclined to resist having to pay to support churches they did not believe in. In this way, the Great Awakening led to more of a desire to keep church and state separate.