Rabbits eat pellets and hay. Not veggies, as they are not good for them. And they should only be fed strictly as treats. And no rabbit can survive on 1/4rth of a cup of pellets at a time. Unless its a dwarf, you end up with a skinny, out of condition, unhealthy rabbit. Most rabbits will eat up to a cup of pellets per day. they will be just fine on it.
Now to answer the OPs question. The answer is no. They can be caged separately, in the same building. But rabbit cannot eat chicken feed. Its not good for them. chances are it will make them sick. Plus they can get coccidiousis from the chickens. Which is something that can also make them sick, and they can easily die from.
Rabbits also have a tendancy to be territorial. They will kick, and bite, and can easily hurt the chickens.They are an animal that tends not like other animals in their space. which is why most are solitary. And a lot of them can get protective and even cage agressive of their territory. They are better off when given their own space. If you want to keep rabbits, I suggest purchasing some rabbit hutches, and keeping them in those. you'll want to fix it sd the chickens don't have access to them.
Ducks and chickens will eat rabbit pellets. They are OK as long as they aren't medicated. When I was in 4h we fed our market ducks and geese the extra rabbit pellets to help fatten them up, and condition them out a little bit. But they can only have a small amount at a time. Works kind of like a conditioner.
