No, the camera only works with a power connection. The descriptions and data sheets at Galaxus are sometimes subterranean. The same applies to the dimensions of the products. It is always best to check the manufacturer's website. I don't know which intern writes these.
Best regards

As already commented on by various parties - the "Aqara Camera Hub G3" does not have a battery. Power is supplied via the USB-C connection on the camera. The corresponding power supply and USB-A to USB-C cable are included in the scope of delivery. Recording is either to an SD card in the camera (not included) or, in the case of an Apple Home Kit application, directly to the iCloud.
'strupilino' has already mentioned it. Some of the product descriptions from digitec/Galaxus are really subterranean. Without checking on the manufacturer's website with the respective manufacturer's product number, nothing works. In this case, not even the product title is correct. Management should definitely keep an eye on this.

No, not possible ...

That would be new to me, I have two of them and since they are also a Zigbee hub I can't imagine that.