They definitely have buttons at GK, but I think whether or not you get them is one of those wacky situations where it depends on the server you get. They used to just hand them out to everyone years ago, no matter what age, and then they started 'deciding' who to give them to, i.e., kids, people with birthdays, etc. And then it got to a point where adults had to start asking for the buttons. When we were there either last year or in 12/07 (can't recall which meal it was), my friend was wearing her DLR b-day button, and the Goofy's crew came out to sing the little birthday song (badly) and bring her the birthday cupcake and they handed her a Goofy's button. Another time in the last two years, I just asked them if we could have buttons.
For the record, when I and two of my friends last ate at the Storytellers Critter breakfast, I had to ask the server for buttons there too. So it is not just GK where this happens. I think they used to hand out so many of them to everyone and people would leave them behind or ruining them, and it probably costs money to have them made. So they don't hand them out in some of these places now unless someone specifically wants them.