Yes, my flock carries too much fat, and one died of fatty liver hemorrhagic syndrome. I have never been big on treats, or so I thought. However, I threw several pounds of seed to make chicken pasture and sadly, I’m pretty sure that’s what made them fat. That combined with access to high protein feed at all times (except while roosting... no feed in the coop.)Overweight is one of the concerns. Plain rice is unlikely to to make them fat.
It's the accumulation of fat on the internal organs that is the problem and we don't see this until they die and a necropsy is done.
The problem with treats isn't so much that it makes the chicken fat, it's they don't eat as much of the food that provides the correct amino acids, vitamins and minerals. Diet health is about variety and balance and a little knowledge of the nutrient content of the foodstuff.
There are certain foods that give the required range of amino acids to make a complete protein.as well as the enzymes needed for digestion. Meat, fish eggs and milk are obvious ones. Dairy produce isn't something that a chicken would normally eat, so that leaves meat and fish. You could remove all the grain feeds and assuming the chicken free ranges just supply meat and they would be fine. The vegetable content they need would be acquired in forage.
Meal worms for example provide a complete protein but are very high in fat. In normal feeding for a chicken be it feral of or one of the breeds of game fowl large quantiles of any individual foodstuff are rare. Chickens are foragers and as such tend to find small amounts of whatever they eat, not a dinner plate full in one sitting.
Their digestive system is different from ours in that it is constantly on; it's designed to cope with constant input during the day and while they are resting the food in the crop drips into the digestive tract overnight.
It's about supplying a balanced food even as treats. A chicken with a crop full of rice will feel full but rice doesn't have all the essential amino acids to make a complete protein. The same applies to pasta and most other foods. They need to be mixed with something else.
I believe @micstrachan could tell you some sad stories about giving too many of the wrong kind of treats.
A little of just about anything is fine; platefuls of food that doesn't have the correct nutritional content isn't.
Unfortunately this isn't a message many want to hear. People like giving their chickens treats but the truth is they are often shortening the chickens lifespan.
So now they are on a diet in hopes I can prevent last year’s chicks from getting fat and can slim down the older ones. I’ve been rationing feed and recently switched them back to layer only, since even my oldest bird will lay on occasion. She had stopped laying almost two years ago, but started back up after dieting.
So, yes, letting your chickens get fat can be deadly and heartbreaking when you understand it was your fault. I don’t recommend it. My girl who has health problems is “insulated like a seal” according to my favorite avian vet. She’s a bit of a glutton, but I’m hoping the diet changes aren’t too late for her.