Important note: Sleep is way more about consistency than anything else. Caffeine has a definite effect, but the most important way to keep getting good sleep is to create a consistent bedtime and wake up time every single day, even weekends.
I had high anxiety coupled with horrible sleep issues. I dropped caffeine for a year and a half, and it seemed to help. I now drink it occasionally, like every friday or so when I know I don't have to wake up early the next day. Like I said though, the biggest factor was creating a strict sleep schedule that I adhered to every single day.
I'm really not sure if there's a strong connection, but man, it feels super nice to not feel addicted to the stuff. Once you're off it and you have a solid sleep schedule, it really doesn't feel like you actually need it to feel awake.