Would a dislocated shoulder be really bad for a quarterback?

Unfortunately yes: Young males who are involved in contact sports have a high rate of redislocation with a non-operative approach. Therefore, most quarterbacks would need surgery on their shoulder. To throw a ball, a significant amount of range of motion of the shoulder is required. Surgery for a dislocated shoulder may result in a mild loss of range of motion which may inhibit the quarterback's ability to throw.

Yes: A dislocation of the throwing arm would be a season ending injury which may need surgery and extend pt.