No, my larger pens are not covered. They are over 50' wide so nope, the largest about 2500 sf. in area, so pretty much impossible to cover. We have large oaks here and I have roosters who are great sentries so I still haven't lost any birds to hawks.
Do you have bantams? They would be more vulnerable to hawks, of course. I have one small flock of bantams but their pen is covered with wire and they only get out of it rarely, plus have lots of places to shoot under for cover (two roosters with those and they are super alert).
Here is the bantam's covered pen and my old hens are in their former pen, also wire covered.
the former bantam pen, now housing elderly hens who can't be with a rooster.
Yes, I have Wyandotte Bantams and my roosters aren't real aggressive. I tried the string and cd's and found a dead hen the next day. :-( My small flock has been on lockdown and we're in the process of putting netting up - hope it helps.......no more free ranging for a while.....