Baby chicks, grown chickens, dogs, cats, practically any animal can possibly cause medical problems to humans. It doesn’t happen very often but it can happen. The general recommendation is to wash your hands thoroughly after handling animals, especially if they are sometimes outdoors.
How many of us actually do that, wash hands after petting a dog or cat? I don’t, even if the dog was just outside rolling in who knows what. Let’s stay real.
One of the risks from handling baby chicks is Salmonella, which can be transmitted through feces. Baby chicks poop a lot and no matter how clean you keep the brooder they will be exposed to feces. There are different strengths of salmonella. People with strong immune systems handle it better than people with weak immune systems. Plenty of people handle chicks and immediately put their fingers in their mouth or lick their fingers. Some people kiss baby chicks. Very few people get sick from this, but some do. That salmonella bacteria is not everywhere, but if it is present you and yours can be affected.
I’m not saying it was caused by salmonella bacteria. I’m saying it might be salmonella, it might be something else entirely, there are a lot of bacteria and viruses out there. I’m not saying it was caused by the chick, there are stomach viruses going around right now. You asked if it were possible, so yes it is possible. And a good way to reduce the chance of infection is to wash your hands with soap and water after handling chicks. Don’t count on sanitizer, use soap and water.
Most chicken diseases caused by bacteria or viruses do not affect humans. Most diseases that affect humans do not affect chickens. Most diseases are pretty species specific. But like the salmonella, it’s possible if you come into contact with a chicken disease somewhere else you can bring it back to your flock. That’s why it’s generally recommended to wear specific shoes especially when taking care of your chickens, don’t wear the same shoes or even clothing you wear to a feed store or to look at someone else’s chickens to avoid bringing diseases back.