Being social is a big part of life. If you can't function well socially, which SA inevitably leads to, then you will eventually become depressed. I have yet to meet a person with SA who doesn't suffer from depression. I think it is inevitable to not be depressed when you have lived with SA for a while.
I also agree with the yes comments above.
Being considered "not normal" in our society and not being able to do things expected of us properly can lead to all sorts of negative feelings of unworthiness, sense of failure etc. which can then easily trigger the depression.