Probably. If you’ve ever been under anesthesia then you’ve probably noticed the difference between sleeping under anesthesia and sleeping under normal conditions. Personally, I normally get the feeling that time has passed when I sleep, I didn’t have that feeling when I had my wisdom teeth removed; and anesthesia still doesn’t turn your brain all the way off. I’m pretty sure if your brain actually turned off all the way and then turned back on again, then you’d probably feel like you’re a different person.