Yes you can but it doesn't taste pleasant in my opinion. It could be used in desserts such as lassi and jam. Some people even put it in salads. I'm not sure if it's used in meals though. Also it contains urushiol oil which is what is in poison ivy and causes rashes. Some people can stand it and get go reactions afterwards but others can't. Better to be on the safe side though because the peels are toxic and have negative effects. Depending on someones reaction to it, they will use it in cooking somehow I guess.
use unripened green mango with peel in Indo-Pak chutneys and pickles as well, plus there is a whole genre of cuisine for "kairi" (that's Urdu/Hindi for the raw mango). But generally mago peels act as poison ivy, it can make one feel ill.