Because screws are typically made from carbon steel wire, they can rust. So, there is no promise that the included screws you are given will never rust. With that being said, however, there are ways to avoid rust.
It all comes down to understanding what causes it in the first place. Otherwise known as Ferric Oxide, rust occurs when water, oxygen, and iron combine. So, if you leave your bike water bottle holders and bike in the elements, then the screws are going to rust.