No, Rust can be still slow (slower than well-optimized garbage-collected languages) if you perform memory allocations on the heap all over the place, ignore cache coherency, use #[derive(Clone, Copy)] everywhere, and use Rc<T> and Arc<T> to solve all your typical ownership issues (plus making the wrong algorithmic/data structure decisions). Language is only a tool, you don't automatically write fast software by using a "better" language.

That said, I think the design decisions of the Rust borrow checker leads most developers either to write borrow-checker-agnostic code by using indices and Vec<T> instead (see https://kyren.github.io/2018/09/14/rustconf-talk.html), or go ham with Rc<T> and Arc<T> until the language basically becomes similar to (but slower than) garbage-collected languages like Go. The former leads to performant code but makes you question why you are using Rust in the first place, and the latter leads to slow unwieldy code and also makes you question why you are using Rust in the first place.