I also have trouble with sleep. However, I can fall asleep rather fast but wake early getting only like 2 or 3 hours a night. I also ruminate on things when I wake rather than before I sleep, like you do. Although it's quite possible, I think it's just a simple symptom of the GAD and not a hint of a deeper issue...for me at least....I'm also bipolar and both together seem to disrupt my sleep......