Can obesity lead to social anxiety?

Yes. If a child is self-conscious about his/her size, then he/she may decide to avoid contact with peers, and to avoid being seen in public.
Yes. Obesity can sometimes be associated with a poor self image and a lack of confidence, and either of these will certainly increase the likelihood of developing social anxiety. That said, many obese people don't have social anxiety disorder, and many people who do have social anxiety disorder are not obese. One does not automatically lead to the other.