It depends on what kit.
As above, if you have an AIO it comes with a gateway. An AC connected PV system (aka another inverter, mains connected) can be linked to the gateway - to allow the PV to charge the AIO's batteries even in a powercut. Once the batteries are full and assuming not enough home demand, the AIO will raise the voltage to "slow" the PV down and eventually stop it from outputting (as if the voltage is too high, inverters have to stop producing electric).
If you have a GivEnergy hybrid - they also can charge the battery whilst the mains is down. However if the battery completely empties, I'm not sure if solar the next day can start up the inverter again.
Then if it's just an AC connected GivEnergy ("AC3" for example), with separate AC connected solar inverter, no, that wouldn't charge up during the mains outage. The AC connected inverter would see the grid has gone and it would stop outputting (aka it is grid tied - and follows the grid's frequency).
The battery on the GE AC3 can output to the EPS socket and/or EPS circuit board if those options are taken during install (or at a later install), but PV charging not an option*
( * I think some solar companies may have their own version of the GE gateway that gets around this).