No do not try and see if they like it. whatever is in their cage they think they can eat, they don't know if that is poisonous and it could also hurt them.I'm just back from the allotment, thought they were cabbage family but don't recognise the stem of these which look quite thick. As long as they were purchased from the veg counter then I would say offer them and see if they are consumed or disgarded.
I don't know its hard to see from the picture. I recommend not feeding it to them and just stick to things that you know they can eat like, carrots, lettuce, zucchini, cucumber, and more. They also can have grass from your yard if it has not been sprayed with chemicals. Hope that helped!I at first thought it was lettuce or mustard greens. But later realised that it's neither. They had eaten a bit but I took it away from their cage. Do you think it can be escarole?
If in any doubt dont feed it, I remember many years ago my flatmate giving our degu a spicy mooli radish because he thought it was a parsnip when he bought it... that was one angry degu!