Yes, the CMs do tell you to go ahead, wear your button for your whole trip. But...there's only one thing wrong with that. You tend to think that all this wonderul, magical stuff is going to happen. And it doesn't...not all that much.
My dd celebrated her 6th birthday, on her first ever trip to WDW. I did mention this when we booked our room at DxL (POR), each time I made an ADR. Now, she did get a nice birthday cupcake and card at the CP, and a birthday song. Other than that? Nothing.
Fast forward to her 13th birthday....2 years ago. Again, she was there, on the day she turned 13. She, and her friend who's birthday was the day after we got home, were given two different birthday buttons...one that said 'Celebrating my birthday in WDW' the other was 'Today is my Birthday!!'..obviously two different intentions. She wore the 'Today is my birthday' button on her big day, the other button on the other days.
I had ordered, and paid quite a lot for, a very special cake to be served at the GF Cafe. It was brought out by a wonderful CM, who got the entire restaurant singing to my dd.
At Chef Mickey's, not her birthday, the girls were each given a birthday cupcake and a special birthday placemat. At the Crytal Palace, on her birthday, they got cupcakes (for breakfast no less!!!).
At HDDR that night, dd got pulled out for special recognition but they do that every night. Still, it was fun for her.
She got many well wishes as she went about her fun in the parks. But, nothing 'huge' happened. No cards in the room, no balloons, no FPs handed to her, no free ice cream, no free dessert other than the cupcakes.
So......while it's nice to wear a button that proclaims your special day, don't get one hoping for all sorts of special attention. If you want something special, plan it yourself. That way, no one will be disappointed.