Absolutely not.

C has the advantage of being an extremely small language in terms of syntax, which means its incredibly easy to port it to any architecture. Whenever you build a chip and want to program it, writing an LLVM backend for it with optimizations is almost trivial (assuming you understand the core concepts).

Rust has a lot more things to consider in the compiler, which leads to slow adoption, and also its more cumbersome to program in.

In theory it could happen, but even so it would take years. There’s just so much C code out there. Stuff like Linux, Nginx, Apache, PostgreSQL, MariaDB, SQLite, QEMU, etc etc.