2 different things.. bleached means alive with flesh but just no color, ie, expelled all its zooxanthellae, and yes, corals will make a full recovery if problems that caused it are resolved. It is a slow process though, can take 1-3 months for color to return.
Dead/skeleton is different, depending on the cause of the injury it is hit or miss if it will recover. Sometimes it will continue to spread, killing off the flesh as it moves, or it will stop, have an exposed dead area, but new growth will eventually grow over the dead spot and make a recovery. All depends on the cause and if the cause has been resolved (like getting stung by another coral)