Yes. Rust's compiler, rustc, is a bunch of Rust code that parses Rust syntax into an Abstract Syntax Tree to which it can apply macros, then this is lowered through two levels of intermediate representations, where more Rust code does the type inference and type checking and eventually borrow checking and various optimisations, until eventually it's lowered to LLVM Intermediate Representation LLVM IR, which LLVM will further optimise then produce machine code for the target architecture.

Impressive knowledge o7

What do Rust developers tend to do while the code is compiling? Vote 'Rust' in all the programming language surveys?

I know you're getting downvoted, but seriously, Rust compilation/linking does take a long time, especially if you enable fat LTO. The upside is it's doing a lot more for you than say the C or C++ compiler would. It's a very small price to pay for what you get.

They play Rust.

Of course not, don't be daft! We go shopping for CPUs.

You can kind of compile (a version of) Rust into C and then compile that as well, but I assume miscompiles are common and there's very little checking done. It's used to bootstrap the compiler for Debian.