If you use this expression you will suprise Chilangos in a good way. The expression is the result of a twist to the classic saying lo cortés no quita lo valiente (being corteous doesn't make you less brave). Cortés (corteous) is also the name of the conquistador that took over Tenochtitlan (Mexico City). Cortés captured Cuauhtémoc, the last Aztec emperor, and tortured him.
The expression lo cortés no quita lo Cuauhtémoc means that being well mannered does not make you more civilized, since from the conquistador's perspective Aztecs were not civilized. That's very ironic given that it was Cortés who tortured Cuauhtémoc trying to get information about an nonexisting treasure.