In places like Germany it's supposedly becoming more common to have a solar panel on the balcony and use a similar plugin device. I think the legal situation in the US is more tricky unfortunately
Yes - such devices need a constant grid output to sync to. When the grid drops, their output drops. Furthermore, at 800W, it wouldn't be able to put any voltage onto the grid even if it tried to as it would get overloaded (it'll be trying to power up the entire neighborhood).