No, the Anthropocene serves as an indicator that non-natural processes shaped its ecology and geological processes. There will be no coal from the Anthropocene era because trees are no longer allowed to fall in bogs. there will be no oil from the Anthropocene era because there will not be large pools of organic matter experiencing titanic compression. For someone entirely hung up on it's not about us he sure seems to see the world through a filter of how can i make this about us.The idea of the Anthropocene is an interesting thought experiment. For those invested in the stratigraphic arcana of this infinitesimal moment in time, it serves as a useful catalog of our junk.
We could last 10x longer than we have and won't leave an appreciable mark. We aren't even a sliver of strata, and most likely all evidence of that sliver will be eroded away or churned under. I think the argument is that we ought to be detectable outside of our time to be a epoch. We can't be sure that intelligent dinosaurs didn't write software for a few hundred years.
By that definition the Holocene doesn't get an era either. But it does. We aren't even a sliver of strata yet but that's because we're still at the top. The K-T Boundary is a sliver of strata and it marks the end of one era and the beginning of another.