I dont have any advice or life experience with goats, but I had a neighbor who had a small pig. It shared a building with its own section. The other section housed a flock of chickens. A small opening kept the pig out of the chicken area. It had a larger opening for everything to go in and out to a free range situation, open all year with no door.
Now this would seem to be an invite for every chicken eating critter in the area to come for dinner in my opinion....but.., he never had a problem with day time or nighttime preditors. I looked it over and it left me bewildered and scratching my head.
I am not promoting this kind if set up by any means, just telling the story as I saw it.
I live a half mile away and was always loosing chickens to something or other
Then after 7 or 8 years, The pig died.
Then he started loosing chickens, untill eventually within a few months, he had none left.
Was there something about the pig that coyotes, foxes, racoons, opossum, weasel, mink, etc did not like?
Maybe the smell.
One small pig with a large area to me, had no aroma like confined pigs do.
Was the pig actively protecting the chickens?
Maybe some pig owners can shed light on this for me.
For your situation, I dont think a goat will be a deturent for a hawk tho.
I've had them swoop down and snatch a chick from its broody mother 6 feet from where i was standing.
Over head netting seems to be the only truly effective way to keep them out of the chickens area.
Good luck and enjoy your goats and chickens.