This claim could kind of go in either direction, because while it is true that caffeinated drinks can lead to fatigue if over-consumed or consumed at the wrong time, there isn't a chemical component in these drinks that will inevitably cause this. Your article provided, Live Strong, is not a primary source that held a true experiment or study with Celsius or other caffeinated drinks, instead it made weak claims that sort of tie in to the main idea but also don't. The author is does not have experience in any form of science, especially not nutritional science, which can be a tell tale sign that they don't have the credibility to make these claims. The underlying truth of the article is that if taken at the wrong time, or if taken too much, caffeine can seriously mess with your body's ability to sleep properly which in turn leads to fatigue and brain fog. It does not say, however, that these drinks will cause this. So in a way your claim is true, caffeinated drinks CAN lead to fatigue but only if consumed against the recommended usage.