Surprisingly, no. Most inverters in the EU must come with island protection. Meaning that if there is no AC from the grid it immediatly switches off the inverter or the battery, there is no stand alone operation.

There are some systems that allow it but they are rare here and require the mains side to be fed trough the inverter itsself ensuring it's never back feeding into the grid when there is no power with the same island protection, or less commonly there is a transfer switch of some kind also eliminating the issue. And either should obviously have a main kill switch on the breaker board for emergencies that also switches off the in home power with 1 action.

But most importantly, either of those options is not plug and play and will require an electrician that hopefully does know what he's doing.