Insofar as we do not make the mistake of mixing consciousness with self-awareness, it might very well be the case.
What's the difference? Can you have one without the other? Are they part of a larger whole? I've never met this distinction before.
The distinction is one cognitive level up the scale of awareness. You can be aware of your body, sensation, and what happens around you. And then you can be aware of your awareness, meta-cognition and reasoning. The same difference that there is between thinking and thinking about thinking (i.e., self-reflection).