If i correct mouth breathing at 20 years old, will it also correct my overbite/overjet?

Probably not: Most of your growth has taken place and there is little more that can be changed. I would suggest seeing an orthodontist for an evaluation and treatment options.

No: Correction of mouth breathing in a growing child will often improve the development of jaw and teeth and will make orthodontic results more stable. If you are considering orthodontic treatment at your age, and you still breathe through your mouth or swallow with what is called a tongue thrust, you would want to correct that so that orthodontic results don't relapse back.

Probably not complet: I recommend you see a mayo functional therapist and an orthodontist that work together. This will give you the best long term results. I would hate for you to have ortho only to have relapse because your mouth breathing was not addressed.