Not with squirrels but I’ve opened a carcass of other critters I’ve trapped and tossed the carcass in the run. I generally use an ax to open the intestines up where they can get at them. They take it from there.
The pros are that they are omnivores and operate on the ”do lunch or be lunch” principle. If it doesn’t eat them they will eat it. Even if it would eat them if it were alive they will eat it if it is dead. It’s good protein for them. Meat provides essential nutrients to a balanced diet that they don’t get from grains.
Some potential cons. Depending on how big your flock is they may not be able to strip the carcass. You may need to dispose of the partially eaten carcass. Well actually you will. How are you going to do that?
If you leave the carcass there it may attract predators. I’ve had crows fly into the run to eat the carcass. I’m surprised I haven’t seen vultures in there. Raccoons, foxes, coyotes, bobcats, skunks, possums, many things could be attracted to that.
The carcass can attract flies, the big green ones. If you leave it there long enough for the maggots to hatch, the chickens will get a feast from them, but the carcass will start stinking by then. The meat isn’t really fresh then either, it’s actually rotting, so you don’t want to leave it out there very long.
It takes some management but it’s good protein.