From the UFAQ
Q: If a player plays "State of Emergency" and executes another player, does the executed player still get the move or action (possibly as a a newly-revealed Cylon or as a new character)?
A: (Tim, FFG, to infocynic) Yes.
Q: If a player plays "State of Emergency" and is executed (or reveals as a Cylon) before the SoE has fully resolved, do the other players still continue to gain their moves or actions?
A: (Tim, FFG, to infocynic) Yes, because SoE was played before the 'end of turn' trigger happened, it continues fully.