Maybe. I think C will continue to have relevance in certain niches like embedded development, and that efforts like Fil-C will quietly carry the torch for a long time. C will also continue to have an important role in bootstrapping.

I generally I don't like the "Rust is killing C" meme because a.) I don't believe it b.) C doesn't need to die for Rust to succeed and c.) it leads to language wars and hard feelings. Rust doesn't really do what C does; it's not a lingua franca among architectures. They compete in some niches and not others.