Most ships have room service available 24 hours a day. Some lines are even letting you order off the dinner menu (during dinner hours) if you prefer to eat in your cabin.
You can eat all day if you want. Let's look at a day on the Carnival Destiny:
* Room Service at 6:00 am
* Breakfast in the Dining Room at 8:00
* Still serving Breakfast on the Buffet till 10:30 am
* Lunch Buffet is open at 11:00, I think I'll just have a salad. I'm cutting down
* Lunch in the Dining Room at 12:00 pm
* 2:00 pm, I think I'll have Chinese at the Chinese Grill
* 4:00 pm by the pool, I could use a pizza from the 24 hour pizzeria
* 6:30 pm, time for dinner
* 10:30, let's have a sandwich at the Pizzeria
* 12:00, Midnight Buffet
* 1:30 am, Scrambled Eggs and Bacon on the Late Night Mini-Buffet
* 3:30 am, I'm through dancing, let's another pizza.
* 4:00 am, Honey, how about a Turkey Sandwich from room service. "Shut up and go to bed we've got room service coming for breakfast in 2 hours."
The answer is yes, you can eat anytime you want.