Yes. I do both chess analyzing in my head before I sleep and chess dreaming. I was concerned but it seems like many people in the chess community do so. I played 13 rapid games of 30-minute time control in a day once, and as a result, I saw my first chess dream. I was lucid dreaming all night. I sleep next to a chessboard and that also affects my sleep thoughts.
To be honest, I don't think I play the game itself. Once it is a dream, all I see is a fade chessboard, and I have the slighest of the impressions of what I'm really playing. I think though that my brain is used to calculate when it faces a chess game, and that's why I spend time calculating.
Each game evolves, but I'm sure it never ends. Maybe because it is a draw but I can't remember.
I remember one of my games, which entirely did consist of queenless late-middlegame. I was trying to improve my position using fade impressions of knights and a fianchetto bishop winning pawns, and I really suffered because my opponent played all the best moves. Or I thought so. I woke up many times that night to drink some water and relax because I was ready to cry, and I suffered, sighed, and murmured all night. Indeed that day I had a pretty traumatizing experience due to my mental disorder, or phobia, whatever, it's called gamophobia, and that's why this game was so painful to me. Dreams depict reality. I play chess and I suffer. Perfect combination.
About chess analyzing before sleep, I identify with your thoughts. I actually see tactics or mating patterns. The thing is I see a different thing repeated and repeated each time. If I see bank rank mate once, I'll see that for the rest of the time I try to sleep. Continuously. If I see the following day a tactic to win a bishop for example, I can't take it off my mind, and I'll see that for the rest of time I don't sleep. Again and again. My mind stucks and prevents me from sleeping.
I really want to consult an expert such as a therapist, just to learn if it's healthy, or I need any medication, or even abandon chess, which I won't, because I love it. But, it prevents me from sleeping well as I calculate and spend the same energy I would spend in a real match. My brain thinks even when it sleeps. And that tires me a lot. I would rather know if gms or psychos dream that too (I don't compare gms with psychopaths dont worry)
Long story short, I don't think it's healthy for me. I don't know if it helps me improve. I think so but I can't really know.
And that's how you know you've been playing too much chess lately - when you're playing the same game night after night in your dream like real life correspondence...