Do symptoms like cyanosis go away quickly?

Depends. Cyanosis is only relieved with oxygen. Total body cyanosis, like from COPD or pneumonia may need supplemental oxygen. If local to a finger like in reynaud's, then will improve when vascular spasm ends and oxygenated blood flow resumes.
Not if one is dead. Typically, addressing the underlying cause with dictate if cyanosis will go away quickly. Why? The color refers to the color or blood and its level of oxygenation- lots of oxygen, then blood is bright red. If low in oxygenation, then it looks more purple. Therefore: 1. Cyanosis from choking? Yes if cause of choking is removed 2. Death? Unlikely.