Ain't gonna happen. Humans live in more environments than cockroaches do.

Oh, we'll decimate the population and destroy "civilization" permanently, no doubt. I imagine that 100 years from now the population will be some tiny fraction of what it is now, and there will be stories of horror unprecedented in all of history (and that's a high bar).

But some miserable humans will survive, to curse our names for the rest of history, such as it is.