The short answer is yes. People often describe their symptoms as feeling like there is no blood supply to the hand. Although the blood supply to the hand actually is not affected, pressure on the median nerve by a ligament does limit the blood flow to the nerve. Because the blood carries nutrients (even to nerves!), if the nerve doesn't get enough supply, eventually, it might not be able to recover. This can lead to permanent loss of sensation/numbness and weakness of the muscles that control the thumb; these together lead to dropping things and not being able to perform fine tasks like fastening buttons, writing, and grooming.