Absolutely. I have GAD as well (in addition to a few other disorders) and I have intrusive thoughts every single day. It sucks, but I just try to focus on good things, and remember that it's just my anxiety talkin'. :-/
Sometimes, it really is scary though, or just disturbing... It's hard to deal with those times, but for me, I just pray. I usually am able to feel better, if not right away, then shortly after.