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! :)

For example Blanchard's textbook (my best guess of what you are using) builds an AS-AD model on top of an IS-LM. The AD equation is a summary of all IS-LM equilibria for corresponding price levels $$P$$. In such a setting a secular decrease of consumption shifts the underlying IS-curve to the left, which yields a new set of IS-LM-equilibria (one for each level of $$P$$) that are all to the left of the equilibria for the corresponding $$P$$ before the secular change in $$C$$. I.e. the AD-curve shifts to the left.
This would mean that you are missing the fact that your IS-LM has some way to go before it reaches an equilibrium after the initial shock to $$C$$, but I am just guessing here since you didn't provide info on your assumptions.
In any case the question should make it clear that the decrease in $$C$$ is secular - i.e. not caused by a change of another variable in the model. Otherwise it may well be a move along the curve.