Can reading help reduce social anxiety?

Avoiding Engagement? Do you mean reading to yourself while in uncomfortable social situations? This would seem like a way of avoiding interacting w/ others in that situation - and avoidance is the hallmark of social anxiety. (People avoid interacting so they don't risk embarrassing themselves - saying/doing something that others might judge them negatively about.) Gr8 documentary on social anxiety: http://ow.ly/F3fzQ.
Probably. Reading can really free you - your mind, your body, and get you to enjoy your imagination. When you read, you pick up ideas and integrate them in your life, and then you can go about discussing them with other people thus bringing you closer into a social circle. Even though it is a solo activity, it can open up new worlds for you and help build your confidence to share these worlds with others.