Place chicken in a 6-quart slow cooker. Top with sweet potato, parsnips, carrots, celery, green onions, sage, salt (if desired), and ground pepper. Pour broth and 1 cup water over mixture in cooker.
Cover and cook on low-heat setting for 6 hours or on high-heat setting for 4 hours.
Using a slotted spoon, remove chicken from cooker. If using low-heat setting, turn to high-heat setting. Stir in gnocchi. Cover and cook for 10 minutes. Meanwhile, cool chicken slightly. Remove meat from bones; discard bones. Using two forks, pull chicken apart into shreds.
In a small bowl stir together 1/4 cup water and cornstarch. Stir shredded chicken and cornstarch mixture into broth mixture. Cover and cook for 10 to 20 minutes more or until slightly thickened. If desired, sprinkle each serving with cracked pepper. Serve with hot pepper sauce.