No unidentified plane would get near enough to a Battle group to be a threat even if it was suicidal, it would be seen early on and shot down before it was anywhere near the Carrier.
Most likely yes, but what a juicy target for our enemies. A plane as big as that could certainly do fatal damage to a carrier. The low odds might be enough if they thought they could pull it off, relying on inertia and luck after being hit with missiles to hit the target.