At a minimum Rust would have to run the C initializers as these are used even in pure Rust code. It might also make use of the security cookie but I'm uncertain about that. Also the C runtime is needed by the SEH handling code (in vcruntime) so Rust would have to replace that before it can replace the C startup/shutdown.
To be clear, this is feasible but it'll require someone knowledgable to put in the work of rewriting this in Rust.