I have broody hens with chicks inside poultry netting all the time. The issues are not what you seem to think they are.
The current is not a steady current. It pulses about 50 times a minute. If it were a steady current it would kill whatever touched it because they would not be able to let go. But since it pulses they can let go. The shock kind of throws them off. Trust me, if you are bitten by that current you will turn loose and so will anything else that can. I've never had a chicken injured. I have seen an adult touch a hot wire with its beak, comb, or wattles. It squawks, jumps back and up about 3 feet, and then resumes foraging.
I have had three snapping turtles caught in the netting. Every time the current pulsed they jerked. After I got them loose two of them eventually wandered off. I never found bodies so I assume they were OK. The third one died, may have been there all night. A five feet long rat snake once got in that netting. I guess it tried to go forward instead of back up. It died. I found a couple of dead frogs in that netting, my guess is that it takes too long for them to jump away. Once I found an adult possum tangled in the netting. I think it just got tangled up and could not get out. Possum are kind of slow moving anyway. It died but it wasn't the electricity that killed it. It was still alive when I found it. I won't tell you there is no danger, especially if the critter is slow moving. I will repeat I've never had a chick or chicken injured by it.
With electric netting each horizontal wire except the bottom one on the ground is a hot wire. The soil is your ground. For a critter to get shocked they have to touch a hot wire while also touching the soil. A predator's fur insulates it but the bare soles of their feet, a tongue, or nose conduct electricity. Many predators can jump over the fence but that is not their first move. They inspect it with their nose first, get shocked, and run away, usually to not come back and try it again. Some people put peanut butter on it at first to encourage them to lock it and get shocked so they can run away and not return.
Young chicks can go right through the netting without getting shocked. Their down or feathers can insulate them but that's not what protects them. The chicken netting holes get bigger as you go up the fence. To get through a hole they jump up, land on the hot horizontal wire, and go on through. They never touch the soil when up there so they do not get shocked.
The chicks can go through the electric netting but the broody hens cannot. Some broody hens let their chicks go through but most call them back to her. I don't know what your broody hen will do so I don't know how much risk they are in.
My full-sized breed chicks can get through that netting until they are around 7 to 8 weeks old. I've had a broody hen wean her chicks at 3 weeks though some wait until over two months. I sometimes have 5 week old brooder raised chicks in there, no broody. I have had some chicks that size foraging outside the netting though they always return inside to sleep or to get feed or water. It is not every chick or even every brood. Some years it is really rare, other years more common. It's amazing how different each brood can be. The size and configuration of the area inside the netting plays a part. The bigger the better obviously, but a pen with a narrow section is worse than one more square or at least wide instead of narrow.
It will be interesting to see what 3KillerBs comes up with. I could see electric netting to keep predators out and a small mesh fence inside that to keep the chicks in.
