Consciousness is the state of being awake and aware of one's surroundings but can you still have a sense of consciousness while sleeping that tells us about our sense of self? The simple answer is no. The essence of consciousness is integration; the ability of our brain to jump communication pathways and share information with other parts of the brain.
While you are awake and conscious your brain has the ability to utilize integration. This is shown in the BBC Horizon: The Secret You video. In this video they conduct an experiment where they shock one part of the participants brain and watch the areas of the brain that light up with activity. In the awake brain you see that the initial area where the shock was given is the first spot to light up but from there the lighted areas jump to many different parts of the brain. This is because while the brain is in a conscious state it can use interact in a network and interconnect between different elements of the brain.
However, while you are asleep your brain is still function just not at a conscious state. In the experiment when the shock is given the initial site of the shock is lit up but that is the only area. There is brain activity but it stays localized. They describe it by saying the modules are active and reactive but stay isolated. While you are sleeping the communication channels in your brain shuts down for a while.
This study helps prove that the essence of consciousness is in fact the integration that takes place. To have a conscious awareness your brain needs to be able to talk to different parts to process information and make connections.