Natural intelligence is also not conscious sometimes. Not fully conscious during sleep, completely knocked out by anaesthetics during surgery and such.

Suppose your brain were somehow exploited for generating text, while you are under anesthesia. That would be definitely unconscious.

Though it's possible that parts of your brain are conscious, but have no access to express that because they don't control the body, nor directly receive any sensory information. I.e. that "you" that is unconscious when anaesthesized might not be the only consciousness in your brain, just the visible one.