YES! I personally was driveing along one day and watched a hawk pick up a very large rabbit. I watched that hawk drop that rabbit from way up trying to kill it, I have no doubt after seeing that rabbit size, that a hawk could and would do the same to a cat.

My request to you is be very cautious with them, I do not think they would come down with you there, but you never know just how hungry they are. As far as the mesh fence, I would assume it would be safe, but keep your eyes open. The one i saw took the animal really high and dropped it trying to kill it, (yes I intervined and saved the rabbit)