No. Buddhi, mann ( manas), chitta, ahamkara are four functional aspects ( dimensions) of Antahkarana (The internal instrument) as per Vendantins. This is a functional division of antahkarana, and by such division, a person is able to better understand the workings of antahkarana and have better control over it. Vedantins often use the example of sleep to explain why antahkarana is not the self-illuminating atman. when one is in deep sleep there is no antahkarana activity or conscious thoughts. This is used as the logic to argue that antahkarana exists only in our waking state by Vedantins. Perhaps this argument is sufficient to establish the brain of physical world is not to be directly correlated to vedantic concept of antahkarana. Brain is part of our physical body and therefore these divisions(Buddhi, mann, chitta, ahamkara ) which were created for analysing the antahkarana itself at rather mental or philosophical level do not have a direct correlation to parts of the brain.
Having said that, as per sarira traya principle of the vedantins, one could argue brain is part of sthula sarira and antahkarana it's correspondence in shukshma sarira, but there is no direct correspondence of physical brain to functional aspects of antahkarana. Cerebral cortex of brain seems to encompass all the major functional aspects of the antakarana.
Western science insists mind to be a function of the chemistry and physics of brain. Vedanta holds that the antahkarana perceives everything, including the information regarding physical brain, by the power of the self-illuminating atman. Further, antahkarana holding that the physical brain is a real entity is nothing but Maya or illusion. As per Vedanta, the self-illuminating atman is real, but antahkarana is temporal and illusionary (exists only during wakeful state) and physical brain an illusion created by antahkarana.
Sources for the answer : What does happens to Prarabdha Karma while sleeping?