NO,computer glasses don't necessarily have the anti-glare coating. In some stores, if you want computer glasses for preventing glare, you need to claim anti-glare coating on it which may cost less than $5.
Not all computer glasses have the anti-glare coating. But if you need, you can ask the optician to add it to your glasses lens. Then you should pay extra money for the money, but it won't cost you too much.