No, the chicken isn’t coated in batter and fried. That’s the American version of the dish and we’ll get to that in a bit. Let’s focus first on where the dish got its name.
Bàng is stick in Chinese. To cook bang bang chicken, the bird is first poached or steamed then the meat is pounded with a bàng to separate it into shreds. The shredded chicken meat is then tossed in a spicy sauce that includes chili oil among the ingredients. So, bang bang chicken may either refer to the stick or to the sound made when the chicken meat is pounded with it.
When the dish was adapted by Chinese-American cooks for American diners, it took on a new appearance that required a different set of ingredients and a different cooking method.

Instead of poached shredded chicken tossed in seasoned chili oil, there’s battered and fried chicken fillet tossed in a mixture of mayo and sweet chili sauce.
I like both versions, to be honest, and I have recipes for both.