Yes, they can.
Quote:
“Social phobia, or social anxiety disorder, would be expected to be relatively common for those with Asperger Syndrome, especially in the teenage and adult years when they are more acutely aware of their confusion in social situations, of making social mistakes, and possibly suffering ridicule” - (Attwood, 2006).
Whole article here:
http://www.asperger-training.com/autistic-spectrum-conditions-anxiety-disorders/You seem to be making the assumption that people with Asperger's don't care about what others think of them, when that's really not true at all. Most do care. In fact most Aspies seem to want friends just as much as NTs do; it's just they don't have the social skills to make or keep many friends.
I probably had SAD when I was younger. I perhaps still do, but interact with people so little these days it doesn't get much opportunity to express itself. However, recently there have been a few times when I've beaten myself up mentally over social gaffes.