Yes! And the longer I sleep, the more tired I am when I wake up. Your dreams may indeed be keeping you from getting a quality nights sleep. I used to practice trying to dream more, and I would usually feel like I was awake all night.
Your body goes through rest cycles in which some you sleep lighter while in others you fall into a deeper sleep. You may wake still feeling tired because your body never really got to or finished a cycle where you sleep harder and get the most rest.
Yes, I have tried that myself. Usually, if you have a bad nightmare, your adrenalin rush is pumping which can exhaust you and you can end up losing your energy instead of feeling refreshed.