He's taught basic survival skills to his children but isn't overly fond of showing emotion. Should Overseer Almodovar ever become incapacitated, Allen has vowed to take over the running of Vault 101.
During the quest Escape!, it is impossible to enter the room where the Macks live (except for use of console commands). Viewing Vault 101 in the G.E.C.K reveals that Mack's 'room' is just a short stretch of corridor with no entrances. It is impossible to enter his room due to the fact that he is scripted to become the new Overseer should the current one be killed - this preserves the storyline for Trouble on the Homefront.
One of his combat lines include "The Overseer will hear about this!", even after he becomes the Overseer.