We have done Honeymoon, Anniversary, and birthdays at or close to Disney trips and they will usually do small things to add to your day.
When we made our reservations, they asked if we were celebrating and we told them what the event was, and they made a note on our reservation. I also told the CM who made our ADRs.
For our Honeymoon, we did Cinderella's Table and they added extra decorations and a special certificate. They also brought out a special dessert and took our picture. For our Anniversary, we ate at Blue Bayou at DL and they brought a special dessert and gave DD a balloon. For birthday, they gave DD a button and a special sash when we went to BBB and when we got back to hotel room, there was a special signed photo from her favorite princess! Also, you can add on some special celebrations - decorated room, special cakes/flowers/gifts - but those are additional cost.
It never hurts to let them know what you're celebrating and if your little one wears the special pin from Guest Relations, they'll be the center of the universe as everyone seems to wish them a happy birthday!