I think this would be difficult to observe, because starvation also increases stress hormones which increase motivation. For the most part, brain metabolism remains high in starvation, but other glucose using systems are reduced, to preserve glucose for the brain. Ketones are also used to reduce glucose demands while keeping brain metabolism high. Ancedotally, I seem to be more motivated when fasting or dieting, but more creative when eating a nutritious diet.

Metabolic syndrome, and hypothyroidism (both diseases of decreased cellular energy production) are correlated with reduced intelligence.

Citations:

Intelligence quotient in children with congenital hypothyroidism: The effect of diagnostic and treatment variables.

Pre-morbid intelligence, the metabolic syndrome and mortality: the Vietnam Experience Study.

Contribution of Metabolic Syndrome Components to Cognition in Older Individuals

Cognitive function in non-demented older adults with hypothyroidism.