A not-yet-fully-upstreamed branch maintained by the linux foundation can, yes. But just like FreeBSD has to make an exception to build certain packages with gcc, the kernel can be exclusively built with gcc for the time being. If you're not using musl libc, I guess glibc might also require gcc but that's an unsurprising coupling, likely due to gcc C extensions in use.
The important points are that such a distro will quickly improve the situation of clang and libc++ compatibility across the board and exercise the alternative toolchain a lot more. In fact, there isn't much incompatible code out there, and it's been fixed mostly due to efforts of Debian, FreeBSD and of course Apple and Bitrig and Gentoo. FreeBSD is the leading force behind making lld a viable alternative to binutils ld and so far ThinLTO (which works with binutils, to be clear) is exclusive to llvm, so there's that.