Can a facial fracture on the cheek cause permanent damage?

Yes depends extent: Certainly, the cheek bone aka zygoma also supports the eyeball (globe). A fracture of the cheek bone with displacement can cause permanent deformity with a depressed or less prominent cheek bone as well as injury to the nerve to the mid cheek, nostirl and upper lip and can also cause vertical displacment of the globe with double vision & increased orbital volume with a sunken appearance to the eye.

Cheek fracture: Fracture of facial bones can cause permanent deformity with depressions in the area or asymmetry between two sides of the face. It might not be apparent early on but with time becomes more obvious. However, not all cheek fractures need to be fixed. You need to discuss with the surgeon to find out if you need surgery. Also facial fractures can cause permanent numbness at times.