I wouldn't think so. It's not like Rust in FF replaces slow Python or Java code, it replaces heavily-optimized C++. If anything, Rust would likely impede speedup efforts (even if it might improve overall code quality and safety).
Also, I believe the project to rewrite the entirety of Gecko in Rust has long been abandoned.
How much of SpiderMonkey (JS engine) is Rust? AFAIK, besides the bindings, it is still mostly C++ and my guess is that it would be difficult to get the core parts in Rust without a full rewrite.
