There is some scientific evidence that it does. And a physiological explanation as well.
During fasting, there are several things happening in the body, among other things hypoglycemia (low glucose level in the blood). All those changes that occur actually stress the brain. That stress has been shown to be compensated by the brain by creating brain-derived neurotrophic factor (BDNF).
"BDNF acts on certain neurons of the central nervous system and the peripheral nervous system, helping to support the survival of existing neurons, and encourage the growth and differentiation of new neurons and synapses" - Acheson et al 1995
"BDNF itself is important for long-term memory" - Bekinschtein et al 2008
BDNF is also one of the most potent chemicals in the body to stimulate neurogenesis (the creation of new neurons), even in adults.
However, as far as I know, there have not been any experiments directly testing whether or not cognitive capacity increases with IF. I.e. only increased levels of BDNF have been found, and IQ and other direct measures are yet to be tested.