I can't remember if there is a graduation specific button, but there is an I'm Celebrating button that you could ask for if graduation isn't available.
If they wear the buttons they will get plenty of "Congratulations" from castmembers. You can also note it on dining reservations or just let the CMs at the podium know about their graduation when you arrive at the restaurant.
The only thing the buttons will guarantee is plenty of verbal "congratulations" from CMs. At restaurants they might get a complimentary cupcake or dessert, confetti on the table, maybe a card but nothing is guaranteed. It depends on the restaurant and your server. Everyday thousands of people are celebrating a special event in DW - birthday, graduation, engagement, wedding, anniversary, life changing moment, first visit - so there is no way to guarantee that everyone's special event will be recognized.