human biology - Does the brain and the body use the same energy source (glucose/ATP)?

While in general the answer is "yes", the brain does use the same type of resources as other parts of the body, you cannot from that alone derive conclusions about the brain competing with other organs. Also, I think that cognitive performance is not a function of availability of resources. In fact, the moment that the brain lacks crucial resources like oxygen, it simply shuts down. But you don't faint when you start running (if you do, go see a doctor). "Power-saving mode" for the brain is not "reduce IQ by 20 points", but "just make sure the body is breathing and shut down everything else".

Also, I do not think that digesting food requires any comparable amount of energy that it would require the brain to give up on some of the oxygen it needs.