It is pretty easy to embed LLVM into an app and use it to generate IR code and then JIT and run it. The Kaleidoscope tutorial creates a JITting repl in just a few hundred lines of code.

Embedding the Rust compiler would be pretty difficult, especially if your compiler isn't written in Rust.

I think that using Rust as a compiler target is a completely goofy idea. But perhaps Rust's MIR intermediate representation could work for other source languages.