Can a family member recover from brain damage due to an hemorrhage?

It depends....: Was the hemorrhage associated with a stroke? How large was the hemorrhage? Was the hemorrhage subdural (more likely venous cause) or epidural (more likely arterial)? Was the blood evacuated quickly or was it too small for surgical intervention. Was the hemorrhage associated with hypertension or an aneurysm? In general larger hemorrhage and association with a stroke suggest a poorer outcome.

It is possible: The location and size of the hemorrhage are important in determining the outcome. There invariably is "brain damage", the question is whether there are significant neurologic deficits. The age of the patient, and whether or not surgery was done are also factors.