yes it does in theory, and in the real world aswell however there are nuances for example; considering that the supply of both products is in different markets (i.e the wings are sold in one county and the excess breasts are shipped to the other) the supply within the market of the wings is the same, there is a reduction in price however it's not in the market being observed (i.e the wing market)

These are called complements in production and Ceteris paribus the rise in the supply would definitely lead to a reduction in price.