No. Once you become Cylon, you lose the 2nd order. You could use the first order to cause Havoc and then the 2nd action to reveal.
WHat kind of Havoc is it actually possible to cause before revealing? Apart from attempting to waste a scout, I can't figure out much more to do... Yeh, if youre in communications, then sending civ ships in a wrong direction, or wasting a nuke 1 turn before scheduled jump. Or use Admiral's quarters or President's office. Is there more?