Yes. Full buffet breakfast is available in Glass Brasserie for Diamonds. However, proper coffee is $5. Brewed, no charge.
It's kind of outrageous to charge for cappuccinos, especially in Australia. I've stayed in several Hiltons in Asia (recently Vietnam), barista cappuccino is actually included in the breakfast.
Plus there's plenty of great cafes around Sydney CBD.
(Please note: this is before COVID-19)