https://github.com/mystor/rust-callcc is callcc for Rust. Technically abuses a feature for a purpose it was explicitly not intended for, but meh :)
callcc and gc are usually not useful operations in rust. That doesn't mean that its not possible to implement them. The implementation might be annoying to use, but of you are codegenning to rust this doesn't matter.
Yes, some semantics won't copy over. I feel like most would though. Those that don't can often be emulated at the lower level with enough codegen.