Kinda? You'd expect flat bands from putting a copper atom into a big insulating supercell. The population of the d band is interesting, though. I don't find it super super compelling, but it's certainly not nothing.
Yes, given the Cu atoms seem to be ~8 Angstrom apart the flat bands are to be expected. So its not clear what "special" about these, given if you just had dilute Cu impurities in some otherwise insulating I'd imagine you'd have something similar for the Cu d-bands.
