Solar Panels can and do work during a blackout as long as the solar panels have charged the batteries before the blackout.
If there's a blackout and no sun is shining on the solar panels then no you won't get any electricity being produced from the solar panels.
When the solar panels are not getting sun they won't produce electricity or charge the batteries so you can use the charge in the batteries until the batteries go dead.
Then you'd have to wait again until the sun came out to charge the batteries again or to allow the solar panels to produce electricity again.
My solar panels work during blackouts and cloudy days because of the batteries and when it's just partly cloudy the solar panels I have do produce some electricity although they do not produce electricity at full power.
Still solar panels are a nice thing to have as a backup for power outages and as long as the sun is shining you'll still have some electricity.