It is my understanding that if, say, boomer becomes a cylon than her every turn abillity can still be used. Furthermore, she can still use her once-per-game ability. This makes Boomer an excellent revealed Cylon, but not a very good unrevealed Cylon.
However, not all players seem to be very equal in this regard as Rosilin (a great hidden Cylon) does not seem to have any power-transfer abillity (she could play a quorum card, but those are all good). This makes Rosilin an excellent hidden cylon since she can do what amounts to Caprica every turn -- with both fleet and jump steps (most of the jump steps can be avoided, but sometimes the fleet steps are really nice).
Basically I want official clarification that cylons keep their abilities when revealed.