If you don't have alternatives, a distro can package rustc-X.Y with versioned names and have a rustc package that conflicts with the rustup package and the rustc package provides symlinks. I believe that's a fairly standard way of packaging compilers?
Though, I agree with @notriddle, in that distros probably have a way to deal with alternatives/conflicts in a reasonable way at this point. If they don't, rust (at least) won't be alone in causing them grief.