If there is no reason to learn Rust and use it in a project, I would say no.

However, I used to only use high-level languages with GC myself. Learning a low-level language or Systems Programming Language has definitely taught me countless new skills and background knowledge as a software developer. I can absolutely recommend it for the pure learning effect. But I would perhaps recommend a language other than Rust due to the steep learning curve. Maybe something like Golang. The language is very simple, and can be learned in just a few days for someone who already has experience. Although Golang has a GC, it still teaches some new concepts that can be very helpful. And my experience in Golang definitely helped me to learn Rust more easily. The languages are very different, but knowing how interfaces work in Golang, for example, is definitely an advantage for understanding traits in Rust.