The power utility will figure it out pretty quickly in an outage. Either they will be surprised and somebody will get shocked at which time they will hunt down the backfeed source and shut you down OR they will test the service wiring first to determine if safe and then hunt you down! At that point you will very likely be the last one on the system to be re-energized.

Yes, a grid-tied system is supposed to have a cut-off inverter switch to prevent backfeeding the grid. But I think a switching inverter is going to set you back quite a bit more money so you can use your batteries during an outage.