Sure they do as well as any other rose they like the taste of. Try spraying some deer repellant around the area it will work for rabbits too. Of course reapply after rain.

Maybe if they fell on hard times, but I don't think it would be there first choice, but rose hips is rich source of vitamin C.

Rose hips certainly are a good source of vitamin C, but that won't be the attraction (no hips at this time of year) if your rabbit problem is happening now.

They must have thornproof gums...

lThanks everyone. Someone told me human hair is good for deer repellent, I think I will try on the rabbits. Now I have to find something for the chipmunks other than my plants!