If you don't know you fell asleep, does your body still get the benefit of having fallen asleep?

Pretty sure I’m not the only one that this has happened to, but there are times I’ll wake up at 1 a.m., go the the bathroom, get a drink go back to bed….and toss and turn for an hour, totally unable to go back to sleep. Lay there with my eyes open, staring into the dark. Think about getting on FB or Fluther. Changing positions. Just awake.
Sigh.
Then I get up again and damn if it isn’t 4 a.m. so 3 hours actually went by, not just 1. I don’t remember falling asleep, I don’t remember waking up again. I do not feel refreshed, just tired.

With all that, did my body and brain actually get any rest during those lost 3 hours?