No, MinGW uses MSVCRT still, it just uses the really really old one in msvcrt.dll that you're not supposed to use, and because that msvcrt.dll is missing a significant amount of C stuff, MinGW implements the missing functionality on top of it. To use glibc on Windows would require a massive overhaul of it to use windows API instead of linux syscalls.
Furthermore Rust itself uses very little of the C standard library, just strlen and various math functions along with memcpy and friends. Everything else Rust does directly through Windows API.