We have celebrated birthdays there twice. The first time was for my younger DS's 11th birthday. We had a great server - Uncle Tim. After we finished our meal, 4 young teenage girls came and squished in to our table with us. We didn't realize what was going on at first and I thought they accidently sat down at the wrong table. All of the sudden, they started singing happy birthday to my son, and Uncle Tim appeared with a birthday cupcake with a candle. They girls were quite quite giggly about the whole thing; it was very funny! Of course, my DS was dying of embarrassment, especially as we were leaving the restaurant and the girls were wishing him a happy birthday from back at their table.
The last time we were at WDW we celebrated my older DS's 14th birthday. When I made the PS, I mentioned it would be my son's birthday. When we checked in, I mentioned it was my son's birthday. At the table, we mentioned it was my son's birthday to our waitress. She told him happy birthday, then went on to tell DH and I what a pain teenagers were. She honestly didn't come across as being in character either, but sincerely relating to us how her son drives her crazy. That was it. No song, no cupcake - nothing. It wasn't that big of a deal to us, just interesting to compare how different CMs treat celebrations at the same restaurant. My son didn't care - we had a great dinner at Teppanyaki that evening. Our chef went all out. He got people to sing happy birthday, and let my son get behind the table with his chef's hat on for a picture. It was great!