Since probably half the guests in DW are celebrating something - birthday, anniversary, graduation, engagement, wedding, special milestone event - there is no guarantee that something special will be done to recognize a birthday. It will depend on the restaurant and your server. Some will do something special while others won't acknowledge it at all. We've had verbal wishes, cupcakes, special desserts or beverages, confetti, and cards as well as absolutely no acknowledgement at all.
It will help if the birthday person wears a birthday button and let your server know when you are seated. If you want to ensure something special it is best to arrange it yourself so that you won't be disappointed.