The brain actually burns a lot of energy so I think its not unreasonable to expect it to burn the fuel it has access to. There was this study on chess players or something in a competition, I don't remember what the study was called exactly, but they found the chess players despite sitting down the whole time burnt an extraordinary amount of calories.
In China there is even sort of a common saying for this. Generally when someone starts sort of acting stupid or in a daze its commonly related to, half jokingly, as “低血糖” or "low blood sugar"
There are tons of psychological and physiological mechanisms that would activate before reaching literally 0g of glucose if your brain, most that would send you straight into the ER or into complete loss of consciousness.
Dangerously low blood sugar doesn't cause losing the ability to speak or to function that you can ignore and just keep working.
I might be wrong but I dont think the brain actually expends 'more' energy in intensive cognitive tasks in the way you suggest.
"As Harrington explained, "The brain is able to shunt blood [and thus energy] to particular regions that are being active at that point. But the overall energy availability in the brain is thought to be constant." So, while there might be significant spikes in energy use at localized regions of the brain when we perform difficult cognitive tasks, when it comes to the whole brain's energy budget overall, these activities don’t significantly alter it."
"Elite chess players are under intense pressure that causes stress, which can lead to an elevated heart rate, faster breathing and sweating. Combined, these effects burn calories over time."
In China there is even sort of a common saying for this. Generally when someone starts sort of acting stupid or in a daze its commonly related to, half jokingly, as “低血糖” or "low blood sugar"