Yes. If you had a varied enough diet and a true rabbit diet which would include tough fibrous plant material as well as softer stuff like grass you could feed on 100% fresh foods. I did it for guinea pigs for 2 years spring through fall. The problem is they eat
a lot when you do fresh foods due to the water content. I forget the exact percentage increase in weight a horse needs in grass compared to hay but we covered it in nutrition class and it's a big difference. For guinea pigs I was using half my fridge to store greens and dumping entire grocery bags stuffed till they were overflowing in to the cage twice a day for just 4 pigs. To feed a full size meat rabbit on greens would take several grocery bag equivalents. Many of the things you feed would not fit in a grocery bag since it would include branches and such. It's just an example of amount. Without hay you'd spend several hours a day feeding just a trio and their offspring on picked forage.
You might want to look in to chicken/rabbit tractors for a good portion of their greens and fencing off areas of the yard to plant food for them and then let them loose in there. This is my guinea pig herb garden with fencing to move them from section to section with edible herbs and flowers.
http://smg.photobucket.com/albums/v244/ ... oor%20pen/ double fenced to keep big things out and small things in. Bird netting was thrown over the top eventually. They were only put in there for a few hours a day not all the time which limited escape and predator attacks. Rabbits would be too busy eating to dig out. As a plus I grew beautiful patches of edible flowers like this
, the cilantro patch was higher than my waist, and I put a blueberry on each corner with strawberries in between along the outer fenceline.
I really miss having land I can do such things with.
Now if you feed partially in hay you need a mineral supplement because the fat soluble vitamins break down within months in even well stored hay.