Are you talking about a veiled?
If so, I would say yes. The value of their ability to eat greens is really exaggerated. In nature it is a great way to get more moisture into your system, but I highly doubt the greens/fruits are having any major nutritional benefit. I honestly believe that they could even get problems consuming too much fruits, the sugar is not something they are obviously capable of processing and it could have an effect on their organs, like liver and kidneys.
ALL variation is good and the right way to fight deficiency diseases, but it should be in reasonable quantity. I make sure the majority of the nutritional variety is in the gutload, a small slice of fruit now and then. The greens is not a essential part of their diet.