The short answer to your question is yes.

The brain needs a lot of metabolic energy to function (neuro-transmission is metabolically expensive). Its preferred source of metabolic energy is glucose, derived from carbohydrate-rich foods as part of a balanced diet.

If you starve yourself your body will use a storage form of glucose called glycogen. Once your glycogen reserves have run out your brain will use what are called ketone bodies as an energy source. Ketone bodies are derived from fatty acids and are acidic. Over-production of ketone bodies can lead to metabolic acidosis which often has adverse health outcomes.

Once your fatty acid reserves are exhausted your body will break down proteins in muscle tissue to produce amino acids which can be used to make the glucose that your brain needs. Muscle breakdown is not a good thing.

As far as starvation is concerned the "rule of three" applies - three minutes without oxygen is often lethal, three days without water is often lethal and three weeks without food is often lethal.

In summary, starvation is a poor plan, not just because of its effects on your brain but because of its effects on the rest of your body as well.