YES !
I used to wake up more tired than when I went to sleep. It's because sleep is very much an immune system function, and therefore if the immune system malfunctions then the "resting" process is impaired.
Can't avoid this problem, but if you can't get to sleep....apparently sleep researchers reckon that anyone - absolutely anyone - will eventually fall asleep if put in a totally darkened room with a bed. (They use the time it takes as a measure of sleep dysfunction.)
If it's any consolation, I used to have it bad , but it just never happens nowadays.