In principle, yes. SRP (my utility) wouldn't even allow that. When the power goes out, our solar is cut off too. I asked about such a setup, and they said "no". A former coworker got around that (sort of) by having a separate battery circuit that powered some things, independent of the main wiring. I don't recall now what he had on that circuit, but I think that literally he had two outlets in some locations so he could swap plugs to keep (for example) his freezer running.

I suspect different utilities have different rules, so yours in WA may allow what you describe. Though I believe backup generators work the same way, and they allow those. It was just solar, apparently. Or maybe it's because we're residential (i.e. they might not allow an automatic backup generator either).