Has anyone been diagnosed with Social anxiety disorder?
Not social anxiety disorder, but I have major depression, PTSD (which is a form of anxiety disorder) and dissociative identity disorder. It won't keep you from getting approved as long as you're getting treatment and the condition is stable at the moment. The social anxiety disorder might make it hard for you to attend support groups and things like that, so you might want to think of how you'll get support instead - like from this website, from a therapist, from friends, etc. If you're on meds for anxiety, make sure you're taking it as prescribed.
Please note: I AM NOT A DOCTOR. If you want medical advice, talk to your doctor. Whatever I post, there is probably some surgeon or other health care provider somewhere that disagrees with me. If you want to know what your surgeon thinks, then ask him or her. Check out my blog.
To OP, be honest with the surgical staff and make sure your therapist, if you have one already, is open for a referral to verify you are ready for this. best of luck to you!