"I hate to do it, but this is what I post when people ask about if their fishing line or other "non-complete" covering is good enough."
Might I point out...
"As typical of the genus
Accipiter (as well as unrelated forest-dwelling raptors of various lineages), the northern goshawk has relatively short wings and a long tail which make it ideally adapted to engaging in brief but agile and twisting hunting flights through dense vegetation of wooded environments. This species is a powerful hunter, taking birds and mammals in a variety of woodland habitats, often utilizing a combination of speed and obstructing cover to ambush their victims." - Wikipedia
Goshawks are a bit of an exception to the rule when it comes to hunting in dense woodland. Most other species do not hunt in that fashion and require more open areas to successfully capture their prey.
Other raptors exhibit hunting techniques that do not require that level of aerial dexterity.
Red-tails have a very varied hunting style:
"The most common flighted hunting method for red-tail is to cruise approximately 10 to 50 m (33 to 164 ft) over the ground with flap-and-glide type flight, interspersed occasionally with
harrier-like quarters over the ground. This method is less successful than perch hunting but seems relatively useful for capturing small birds and may be show the best results while hunting in hilly country. Hunting red-tailed hawks readily will use trees, bushes or rocks for concealment before making a surprise attack, even showing a partial ability to dodge among trees in an
Accipiter-like fashion. Among thick stands of
spruce in
Alaska, a dodging hunting flight was thought to be unusually important to red-tails living in extensive areas of conifers, with hawks even coming to the ground and walking hurriedly in prey pursuit especially if the prey was large, a similar behavior to
goshawks. Additional surprisingly swift aerial hunting has reported in red-tails who habitually hunt bats in
Texas. Here the bat-hunting specialists would stoop with half-close wings, quite
falcon-like, plowing through the huge stream of bats exiting their cave roosts, then zooming upwards with a bat in its talons. These hawks would also fly parallel closely to the stream, then veer sharply into it and seize a bat. In the
neotropics, red-tails have shown the ability to dodge amongst forest canopy whilst hunting. In
Kansas, red-tailed hawks were recorded sailing to catch flying insects, a hunting method more typical of a Swainson's hawk. Alternately, they may drop to the ground to forage for insects like
grasshoppers and
beetles as well as other invertebrates and probably amphibians and fish (except by water in the latter cases). Hunting afoot seems to be particularly prevalent among immatures. Young red-tailed hawks in northeastern Florida were recorded often extracting
earthworms from near the surface of the ground and some had a crop full of earthworms after rains. Ground hunting is also quite common on
Socorro Island, where there are no native land mammals and invertebrates are more significant to their overall diet. A red-tailed hawk was observed to incorporate an unconventional killing method which was drowning a
heron immediately after capture. One red-tailed hawk was seen to try to grab a young
ground squirrel and, upon missing it, screamed loudly, which in turn caused another young squirrel to break into a run wherein it was captured. Whether this was an intentional hunting technique needs investigation." - Wikipedia
"Swainson's hawks hunt using various methods. Many still-hunt, watching for prey activity from a perch such as a tree, bush, pylon, telephone pole, hummock or other high object. Others hunt by soaring over open ground with wings held in a dihedral, using their stellar vision to watch for prey activity below. It occasionally courses low over the ground like a
northern harrier (
Circus cyaneus) or hovers like a
rough-legged hawk (
B. lagopus) while hunting. They frequently engage in transect-glides while actively hunting in flight. It commonly perches on the ground both during migration and on the breeding grounds. While hunting on the ground, almost entirely for large insects, their gait can appear awkward but they are often successful in pinning down several insects per day." - Wikipedia
So in part, yes the fishing line will probably protect the chickens. However that depends on how well it actually covers the run. Also bear in mind that clear fishing line will be much harder for hunting raptors to spot and they can seriously injure themselves if they fly at a high speed into it.
All that being said, why don't you just cover that whole run with poultry netting and be done with it? That would definitely work and you wouldn't have to worry as much as you are now. I'm getting ready to do mine as well.