Yes. Though garbage collectors can have an indirect influence on the design of the language, that makes it easier to handle data races.

(As an example, image how much simpler Rust would be, if they went with garbage collection. Or how much more machinery Haskell would need, if they went with Rust's memory management strategies.)

I'm not sure what Rust would gain from a garbage collector - it'd still need all of lifetimes for instance, because ownership is the necessary piece for preventing races.