You know that thought didn't even occur to me. I have one like that in my brooder too along with a digital one. I just got my chicks yesterday and IMO they are too tiny right now to break it. They haven't really shown to much interest in it yet anyway, although one used it as a roost for awhile. I doubt this was intentional, she just happened to be on it when she fell asleep. They are so funny, it's almost like they have narcolypsy or something. They just fall asleep at random and a few seconds later pop back up and run around again. I could see where a little bigger chick could cause that concern though and covering it may not be a bad idea.
I am beginning to have the same opinion as some of the more experienced people on the board however, the chicks will tell you if they are to hot or cold and I will more than likely remove at least the regular thermometer in another day or two from my brooder if not both of them. I can have the therm's side by side in there and they will vary in their readings by at least 3 degrees. that drove me nuts when I was trying to get it ready before the chicks came. Now, I think the chicks themselves are the most dependable thermometer to go by!
Good luck and enjoy your chickies!