Can rubber bands correct a skeletal overbite?

Growth. In growing children elastics can be used with braces to guide skeletal growth. In adults both braces and jaw surgery are required. There are no shortcuts. See a qualified Orthodontic Specialist for guidance.
Skeletal correction. If you have an overbite caused by a significant discrepancy in lengths between the upper and lower jaw then rubber bands are unlikely to correct the problem; if the jaw size discrepancy is minor they may help. Rubber bands used during orthodontic treatment act as a force to move teeth only, not the jaws, so if your problem is derived from the jaws then moving the teeth may not an ideal solution.
Yes, but . Yes but not usually until the end of treatment after the patient has worn the braces for about a year.