yes they would..usually any kind of fruit tree especially apples. i used to get the twigs and cut them the size i wanted. then i would boil them in a big pot for 20 mins then dry them on a tray in the oven at around 350degrees for another 20 mins or so. This way you know there are no bugs or disease that can make ur chin sick. My girl loved it and we had sticks to last us through the winter without the expense of the pet store.
I haven't givin them much yet, but I was only giving them new growth twigs. There small and soft and no chance of having bigs in them. They love the strip off the green skin. They have enough hard stuff to chew on.
New growth could still have pesticides if it's been sprayed in the last year. I think I'm remembering that correctly. You really need to clean and bake the wood. There could, and probably are, parasites in the green wood that need to be killed by the baking. The reason for scrubbing is to get any dirt/feces off of it.