As long as CMC remains in effect (there is no Influence removal performed to cancel it), any coup at all anywhere, whether BG, non-BG, event-driven, or "free," performed by a player targeted by CMC instantly loses the game for that player. The loss is due to CMC and not due to DEFCON: CMC itself is a way to instantly lose.
This CMC effect even covers CIA Created / Lone Gunman. For example, if the Soviet player is targeted by CMC and can't remove Influence from Cuba to cancel CMC (presumably because Fidel hasn't been played or he was realigned out and so he has none there to remove), the American can play Lone Gunman at DEFCON 2. Any coup by the Soviet as a result of the Lone Gunman event, even on the American turn, would lose the game for the Soviet due to CMC instantly (if a BG, before dropping DEFCON to 1 and losing the game for the American). There was a CMC on, you didn't defuse it, and you couped, so you lost; DEFCON didn't enter into it.
CMC can indirectly drive a DEFCON loss. CMC drops DEFCON to 2. Imagine the American headlines CMC and the Soviet headlines Missile Envy. CMC drops DEFCON to 2, and then in exchange for Missile Envy the American hands over We Will Bury You (4 OPS) whose Soviet event the Soviet must trigger on his headline phase, dropping DEFCON to 1 and losing the Soviet the game.
In a recent game I played, as the American I headlined CMC and the Soviet headlined Missile Envy. DEFCON dropped to 2 by CMC. In exchange for Missile Envy I handed over Che (I didn't have any 4 Ops card except The China Card). The Soviet actually lost the game when he did not ask questions in chat, ignored the screen warnings, and did not remove influence from Cuba (which was 0/3*), but just went ahead and used the Che event to coup Colombia. I was behind by quite a bit, and he rolled a 6, so it was a welcome result.