Exactly like that. It happens in real-life and no doubt that's where they based it from. It happened to me a couple of times already, the deepest I got was 4 levels.
Real-life sleeping > level 1: sleeping > Level 2: sleeping > Level 3: sleeping > level 4: awake
Usually, it was very bad. A form of nightmare. You slowly get aware of it, even to the point that your brain tells you that you are awake. Then when something happens that you want to wake up (for example, you died, or you suddenly got aware you're sleeping), you will indeed wake up, up to the next level.
Once again, your brain will tell you that you are finally awake.
The first experience I had of this was when I was barely a teenager. It was a nightmare within a nightmare within a nightmare within a nightmare. When I got fully aware I was sleeping, that's when I fought, waking up, then waking up, then waking up, then finally waking up to the real world.
Problem was, I was no longer sure if it was the real world I woke up to. To this day, I sometimes think I am still sleeping.
Just like the other ending in Inception. Hence I love that movie. I can relate.