What a well thought out convincing argument. Are you honestly saying that 'G' exists in a vacuum having no effect on C, I or NE? You have fallen for the Keynesian fallacy of spending oneself to properity. You have to define what you mean by 'quickly' (which no one actually claimed, but you threw in as a straw-man). Would it be immediate? Probably not, but, released from the bonds of regulation and taxation, this economy would take off. And surprisingly soon. Besides, as was pointed out, it could be argued that government spending should not be included in the first place, since it can only spend what it takes from the economy in taxes, borrowing or inflation. So, even if the nominal GDP figure went down, therefore meeting the definition of a recession, the economy would actually be better off (unless your a government moocher or looter).
The assertion does not have support in literature. While the Austrian school contends that increased debt produces diminishing growth over time, there is no basis for the revised equation that removes government spending from the calculation.
If we eliminate the "G" in the equation, then we suppose that government ceases to exist. That includes the military. Is this your position?