Yes, ripening like they do in India will bring out the exterior color so long as it was picked the mature stage of green. Many Indian mangoes are said to be best when harvested this way. Oh, and ripening in camel dung and hay mixture is best. Anyone hot a camel??
Never put a mango in the fridge unless it is fully ripe. In any event, mangoes are best if never refrigerated, they should be sated at room or outdoor temperature.