In the eyes of an adult, yes, it is kind of dorkey. In the eyes of an 2 1/2 year old little boy who LOVES Buzz Lightyear (my son), he loves it. Even my 5 year old daughter enjoys it. There is some audience participation which my daughter really enjoys. My son is shy and usually doesn't participate but still loves it.
No, Woody is not in it and I don't remember the restaurant's name either but it might be the Lunch pad. That also might be the old name, not sure but I believe it's the only outdoor counter service place in Tomorrowland.