For a price, they'll absolutely serve a cake. There's a cake thread on the restaurant board where you'll find all sorts of info about ordering cakes.
If you get a birthday button for DS7 then every CM you encounter will wish him a happy birthday. It'll make him feel really special. That's the only thing that's absolutely guaranteed. Oh, also, at character meals and at LeCellier they typically give a birthday card. At fixed price restaurants typically dessert will be brought out with a candle though if your server is busy it might not happen and isn't guaranteed or even advertised (anywhere but by fans on boards like this that is).
Beyond that, sometimes a restaurant will serve a cupcake and sing, sometimes a CM will toss some pixie dust your way and do a little something special, but these types of things are truely pixie dust and not to be expected.