Is it possible to continue feeding the AC consumers with the battery (without injecting) when the grid has failed?

Yes, if the grid fails and the AC input voltage drops below 170 V (in UPS mode) or the frequency drops out of the window of 40-65 Hz the Any-Grid PSW-H will declare the AC source invalid and will disconnect it completely by mechanical relays. The Any-Grid PSW-H will then automatically act as an Off-Grid inverter within 10 milliseconds and provide power to your loads without any risk of back-feeding into the grid because it is then galvanically isolated from the grid on both neutral and line wires.