If the Cylon loyalty card ability says "If not in the brig...", can the player then activate it when he reveals himself as a Cylon while in detention in New Caprica?
No. Abilities that are affected by the brig are affected by the detention area. The FAQ covers this under Pegasus Expansion (page 2), Brig, Sickbay, Detention Area, Medical Center
If you don't like that answer, the Pegasus Rulebook (page 14) states:
As is the case with the Brig, players cannot use the reveal actions on loyalty cards while in Detention.