Potentially, yes. But if you clean their brooder frequently, and use normal hygienic habits for yourself and anyone who handles them, that should not be a problem. I used to have a bottle of handsanitizer near the brooder and used that on my hands before and after i handled them. Before, because I didn't want to introduce anything harmful to them, and after because I didn't want to introduce anything harmful to me/us from the brooder.
Just use your common sense, millions of people brood chickens in their house and no-one has died from it yet.