Not usually but it's always possible. You will also eventually break arrows that you stuck in the target. Probably by hitting it with the next arrow. The point is, plan for that and get extra arrows. It would be good to also be prepared to retip, renock, and refletch the arrows. Fletching is the hardest, I never actually did that, but I think there are some EZ mode self adhesive feathers you can use.
The roof on that stand is interesting. It might cause more breakage too but I'm sure the benefit of keeping sun and rain off the target outweighs the risk. My only problem with that target is the height. I like to always be shooting down. That way if I have a bad shot, the arrow won't go as far.