Can hyperosmolarity cause brain cells to shrink?

Yes. Mannitol is osmotic agent utilized to raised the serum osmolality and actually takes fluid from healthy neurons to make room for damaged neurons to swell. Another agent utilized in certain institutions is 3% nacl solution which again raises the serum osmolality for the same reason. Osmolarity is mol/kg and osmolality is mol/kg which is what is used in medicine.
Brain damage. The answer is yes as with hyperosmolarity you are withdrawing fluid from the cells and in turn causing them to shrink.