Short answer, yes, I am often more tired upon awakening than I was before I went to bed. Before I was diagnosed, my MD thought I had sleep apnea, in part because of that.
However, it's getting better now that I've been going to therapy for a few months and aggressively working through things. I feel a little more rested than before when I wake up. I can still sleep for 12 hours and be tired, but feel like maybe it did me some good...I don't feel like I was battling something all night. It's as if because I am spending some conscious time on dealing with trauma, my brain can relax a little and not work so hard to process it when I'm asleep.
Lately I've been sleeping with my teddy bear and GloWorm doll from when I was a little girl (I'm 30), and on the nights when I'm not having nightmares, I awaken clutching them tightly, not having moved much during the night. Vast improvement. They're very comforting for some reason.
Oddly enough, I too have no trouble sleeping during the day.