never knew you could mess with the eggs like that. interesting.
most states do require a permit, it is well over 50% maybe 75% of all states in the US. require some sort of permit. carp in general, including koi to grass carp, and various individual species of them. are invasive species. it has been a few years looking at a map someone made, but the few states that do not have laws, are generally hot/dry desert like climate, were there are very few lakes/creaks/rivers within the state.
as far as fish getting out of overflow. (been there done that), 5 to 7lb channel catfish found in a culvert years ago. that came out of one of my lakes.
from regular liner ponds, to aquariums, have seen fish jump right on out of the water and end up dying before i got around and found them at feeding time. with overflows there is not much of a "lip" and water going down them. so it is almost a no brainier for a fish to get startled and just shoot quickly in one direction even if it means coming out of the water completely. and going right down the overflow.
when i have cleaned out the overflow on the lakes here. minnows will go straight down the overflow. if i do not re-set the grates up correctly surrounding the overflows. and slam the water to scare the fish off while cleaning the overflows up.
i have tossed fish on the ground, taking out of basket, and they will hope around 100 foot if they get going in a single direction. give them just a sliver of water to keep water on there gills. and they will keep on going in one direction. till they either die, or get to some deeper waters.
in the creek going through property, have found all sorts of bluegil and bass, and channel catfish. that have come out of someones lake up stream most likely. next large rain storm, they all clear out and continue on down stream.
it is not if fish will get out of the overflow, but when will they and how many will get out of the overflow over time.
i have concrete poured around my overflows. and then grating wall at edge of the concrete. so i can help keep sticks from going down overflow. the holes are 1/2" diameter. i still end up seeing minnows on the wrong side of the grate, along with tadpoles. it may only be 1/2" of water if that. but still there.
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i would not be to worried about all the stuff i did on my own overflows. with grates and like. i got one nasty clog one time. and enough was enough, so i poured the concrete myself and put in the grates, so i never have to ever deal with any clog like that ever again. the grates are not there for keeping fish going out the overflow, but keeping branches out of the overflow.
storm + 1 large tree branch + vertical overflow 30 feet plus deep. then lots of little iddy bitty twigs getting caught on the large branch, and filled the overflow right on up with more and more twigs.