I would absolutely eat cake for breakfast, but that said it wouldn't be my first pick for a few reasons. First, buffets have a lot of dessert options that I like to enjoy so I usually choose a venue for cake where I can enjoy it and not miss out on the many other yummy treats. Second, if you plan to have leftovers you'll be stuck with them the rest of the day or until you leave the park. I usually plan for cake before taking a break for this reason, but it has happened that we thought dinner was the end of our day and I ended up carting around a cake box for a couple hours when we decided we just weren't finished.
As for the singing, we usually get cakes for no real reason, but the one time we had a birthday cake for my MIL (at The Plaza) they did sing for her. Another time at LTT we were having a pirate themed day and ordered a pirate cake and were all dressed in pirate gear. Our server thought it was so cool that she did make a big hoopla about it when she brought out the cake, clapping and making a big announcement wishing us a magical vacation or something like that with every staff member and even the chef in attendance.