Actually maybe not? Iirc most "traditional" anesthesia basically knocks you down to the bare minimum of brain activity to remain alive and reliably regain consciousness (which is why being under anesthesia is usually a "blink and you miss it" ordeal, your brain isn't active enough to be aware that time has passed).

However, if I'm not mistaken, stuff like ketamine or nitrous don't do that, and sedate you in a manner more similar to natural sleep.