Can you leave a dent in your chest without causing long-term complications?

Yes. The "pectus" or dent focused over the breastbone is quite variable & for most is a cosmetic issue. If related to an infant respiratory pbm it may improve over time.Those with marfan or other syndromes have other more pressing issues. Other than shifting the position of the heart, decreasing exercise tolerance & sometimes causing a leaky heart valve, one could live a productive life ignoring it.
Depends. If your "dent" or pectus excavatum is not causing any problems then no treatment may be needed.
Only w/o symptoms. The are many people with pectus excavatum who have no associated physiologic symptoms. They don't require treatment. However, for those with pectus excavatum who do have symptoms of exercise intolerance, repair is recommended. With time, as the chest wall stiffens, compression on the heart and lungs from the deformity will limit cardiorespiratory function.