Does consumption decrease directly lead to a shift in Aggregate Demand curve to the left? Studying macroeconomics I began to wonder about the validity of a certain statement that I couldn't find a clear answer to: 

"When Consumption decreases, Aggregate Demand curve will shift to the left."

First I thought this was obviously right. However, considering the components of AD (C, I, G, NX), when consumption decreases that would directly lead to the same amount of increase in Inventory, which results in the increase of Investment (I). So since the decrease in consumption is directly offset by the increase in Investment, Aggregate Demand wouldn't shift, and GDP wouldn't change at all right? At least, this is the answer I came up with.

If this statement ("When Consumption decreases, Aggregate Demand curve will shift to the left.") was one of the choices for an AP Macroeconomics question where you had to choose the right/wrong answer choice, would this statement be true, or false? 

I couldn't get my head around this statement, and the above logic (Consumption decrease ---> Investment/Inventory increase by same amount ----> GDP unchanged) was the only one I could think of after pondering for hours. 

Is there a clear answer to this statement if this were in an AP Macroeconomics question? Would a decrease in consumption really directly shift the AD curve to the left, or would it remain unchanged due to my logic? I would really appreciate a good explanation! :)
You mention here a crucial point that falls nowadays more and more in oblivion, that is the well-known aggregation issue across consumers. The described behavior of the individual and aggregate demand curve can only be expected to be observed when the essential properties of the individual demand functions can be bequeathed to the aggregated demand function. For this case one needs a particular type of utility function, it must be of Gorman form, that is, the utility functions of consumers must be quasi-linear, or to put it differently, they must be linear in the numeraire good to get an aggregate demand function that inherits their properties from the individual demand functions (cf. Varian Microeconomic Analysis 1992, third edition, pp.152-154).