Yes, these can definitely come with GAD, especially if you've had it over several months or years. The right combination of treatment can help get these things moving in the right direction. Do note that GAD is considered a chronic condition, so even if you do well for a goodly length of time, symptoms may pop up again if you get into stressful circumstances or sometimes stop treatments.
Cognitive behavioral therapy is a highly recommended therapy for anxiety because it helps train your brain into thinking thoughts over time that are less conducive to anxiety. So that can be helpful, I've been achieving some results not in preventing my anxiety but in alleviating it once it's come on, shortening the duration. etc. I'm also on Prozac which I've started to notice a difference in the frequency of my anxiety. However, I wouldn't say my anxiety is under control yet, as I am in a very high stress work situation right now. In the process of getting out of it, but the job hunt itself is stressful.
So, in short. Yes these are very common symptoms that come with chronic anxiety. And yes, with treatment they can improve. I recommend adequate sleep, 7-9 hours per night, light to moderate exercise 3-4 days per week, CBT even if it's at home with a workbook. A fish oil supplement also may help you with mental alertness to some degree.