You can never guarantee that any restaurant will do anything for a birthday. Even if you tell everyone in the place that there is a birthday, it does not mean you will for sure get any sort of treat. If you want to have something special for that meal, then you will need to do it yourself.
Honestly, I worry that you may be setting yourself up for disappointment. It's true that many restaurants do give special treats to those celebrating an occasion, but I don't know of any restaurant at Disney that does this 100% of the time, without fail. If you want to assure that you have a special dessert, the only real way to do that is to order one.
If you're asking specifically about cupcakes vs. cream puffs or another small treat, I can't say for sure except to say that I've never seen cupcakes given there. I think that what they do offer in their dessert case far outstrips those little white cupcakes anyway.