Can a tooth abscess cause permanant swelling and damage to face?

Unlikely. I have seen a draining tract from a tooth abscess extending to the outside of the face on the cheek. However, as the tooth is extracted (too severe bone loss), the area heals well with minimal scarring. However, early treatment will be very beneficial and inexpensive than wait.
No. Facial cellulitis is swelling of the face. A dental infection can cause space swelling that can be visible as an outside swelling of the face. Dental treatment and antibiotics will reduce the swelling with no permanent damage to the face.
Unlikely to bperman. It can cause serious swelling which can be very serious & even life threatening in rare instances. Typically after appropriate treatment, extraction, root canal or periodontal therapy, the swelling will resolve.