The answer is a bit complicated. While I was not entirely sure of this common nickname for the plant, when I looked up an image I realized it is all over the place where I live. I have outdoor rabbits and when they roam, they definitely much on this plant. It is unavoidable. So thankfully, due to my own experience I can answer that YES they can eat it.
HOWEVER, as with all greens you decide to give your buns or let them eat, consumption should remain in moderation even if it is not poisonous to the rabbit. Control the amount they are exposed to. I only let my rabbits much on a few greens to keep their digestive systems healthy. They still have fun hopping about, even if it is not eating consistently. Remember that their primary diet should consist of hay and pellets. An abundance of herbs, fruit, or vegetables may cause your rabbits digestive system to go into shock–and as I am sure you already know, they can neither vomit nor pas gas so this can be very dangerous.
So long as you limit their consumption to a few meager stalks of the plant every week, your rabbits will be fine.
Someone said that this is a complicated question and I wanted to add that it is not complicated at all I just have to see this link about What Eats a Rabbit. You will find there all the information that you need. When I bought a rabbit I was very concerned about it’s product list. It was this site that helped me providing my rabbit with all the necessary products. I think when it comes about pets everyone should take responsibility about how he or she will feed the animal.