I think it really depends on the person, the severity of their anxiety, how the medications work for them, and what they feel comfortable with. In my personal experience (I've suffered with general anxiety, health anxiety, and mild social anxiety and OCD since I was 8) I was able to take medication for about 4 years and then come off of it. I've been dealing with the anxiety for the past 2 years using relaxation techniques and the things I learned in years of cognitive behavioral therapy. I think for me the medication definitely helped to calm the anxiety, also allowed the CBT to be more effective. With the anxiety and irrational thinking slowed down, I was able to really concentrate on the CBT and let the lessons sink in. I developed healthier thought patterns while on the medication and when I decided to go off of it I continued with the healthier thought patterns.
I only went off of the medication (which by the way was Paxil first, Lexapro later) because I felt that although the anxiety was not as strong, all of my other emotions were dulled as well. For me this was not worth it -- but I can see for how other people dealing with severe anxiety it could be worth it. The anticipation of what might happen after going off of medication might also be a trigger for anxiety, which can be a problem.
I guess my point is that I do think it is possible for some people suffering for anxiety to go off of medication if they really want to, and if they've learned good coping techniques while on the meds. But it's really a matter of how severe the anxiety is and how comfortable you feel giving things a go without them. It's definitely something to discuss with your therapist/psychiatrist because coming off of a medication is also hard physically.
If anybody's thinking about coming off of them, I wish you luck!