I don't think so. I would have thought that the Great Awakening was a religious movement which would have stirred people in the 13 colonies into a greater religious mindset, not one where they would have argued for greater independence from the UK. Bernard Bailyn (think that's the right spelling) argues in his book 'Ideological origins of the American Revolution' that the colonists had a mindset which was wired in such a way that when certain events conspired together they would make the move for independence, but religion doesn't really seem to have been a factor in the many arguments put forward by the colonists. Certainly the great awakening did not have any negative effect on the behaviour of the colonists during the 7 year war when they fought eagerly for the British against the French.
I would argue (for what its worth) that the revolution sprang more from a changing policy by the government of the UK after the successful culmination of the 7 year war, to tax and increase the level of control within the colonies which spurred the Americans into action. Certainly the argument of no taxation without representation and the other debates led by the separatist colonists do not make much reference to any religious zeal or differences with the British.