Yes, that's how bootstrapping works. C is still easier to bootstrap than Rust, because it's simpler to implement and requires fewer steps. Of course, you trade off other features for that simplicity.
Bootstrapping Rust would involve the same steps, only at some point you've got to write a Rust compiler in assembly, or write a C compiler in assembly that can compile mrustc, which probably means writing another C compiler in C so you can easily add all the needed features.
Well, if we are going hardcore nothing prevents to write a Ferrocene compliant Rust compiler in Assembly.
Or even better, lets follow the hype, use bootstrap strategies from the 1960's, and use WebAssembly instead, like many bytecode based compilers on those days, having written a macro Assembler instead, thus mapping the bytecodes into macros for the specific home made CPU.
gccrs, the Rust compiler for GCC, is written in C++. If you can compile GCC, it will build the Rust compiler for you.
Presumably the NetBSD project can bootstrap to GCC.
I think they use LLVM rather than GCC, which makes it even easier.