Yes. You're not unconscious when you're asleep, you're just in an altered state of consciousness. Being actually unconscious is a very different experience; if you'd ever been through surgery with general anaesthesia you'd know about this.
Why draw the line at sleep? Your consciousness, such as it is, is pretty fleeting and vague anyway. What reason do you have to think any self survives from one moment to another?
At least while awake, you may be fleeting but you exist in a near constant stream of "you", which make it feel constant. When you go to sleep your brain enters an altered state, which is only a subsection of yourself.
