No hawk has as much as tried. They can easily see they can not get the birds due to the netting. So no: no hawks caught in the net. They simply hunt other things. I still have tons of hawks in the yard all the time, and owls at night, but it's easy for them to see they can not get in there.
Not...
What I suggest is to build a nice big run that is well fenced and predator proof as you can get it, and then put a net over it. That's what I did. Now when the hawks stop by (the National Forest is right across the street, we have tons of hawks and owls) I just enjoy them.
If you watch videos...