It is absolutely possible! Most birds I encounter are overweight (some morbidly obese) due to overfeeding of scratch. Listen here:
Scratch is not good for chickens.
Lots of people don't get this, so I'll go ahead and repeat it. Scratch is not good for chickens.
Think of it like a really rich food - it's the chicken version of chocolate cake. Delicious, and something you could so easily eat a ton of, but nutritionally empty and not at all good in large amounts. That's what it is to chickens. And to continue the metaphor - sure, a bite of chocolate cake each day, or a slice each week, wouldn't be a problem. But you eat a whole bunch of it every day... that's a problem.
I once did the math on this. Most reputable poultry folks will quote 10% of the diet as the absolute maximum for scratch. For your typical mature laying hen, this is 1/2 tablespoon a day. That's not much at all, is it? But if you think about the size of a chicken's body and how much they eat each day, it definitely becomes obvious how that could be 10% of the diet. Any more than that, and you're risking your bird developing nutritional deficiencies, bumblefoot due to obesity, and reproductive issues due to a lack of necessary nutrients and minerals like calcium.
If your hens have been eating a significant amount of scratch recently, and you suspect they are obese or otherwise unhealthy, then I would recommend cutting out all treats and scraps for several weeks. Force them to eat their layer feed and nothing else. After this, you can introduce treats again, but be very careful feeding scratch. Better alternatives to scratch which they will enjoy just as much include fruits and veggies, and even protein-rich items like scrambled eggs or ground beef, in small amounts. Mealworms are a great option as well, but they can be quite fatty, so don't feed them too liberally!