I’m not from Blink, but I can assure you that they work fine with both USB and batteries at the same time, and that they default to battery if power either fails or is removed.
How can I state this with such certainty, well that’s because Blink both state it on their website, and in several replies to similar threads to this one, and second because I’m running two of my cameras in exactly this way, and have been for over nine months, and have tested this functionality extensively.
See here from Blink:
It’s important to note that if you lose power your router and sync module will likely be down as well, so I’m not entirely clear of the benefit of the cameras continuing to run. If you make arrangements to maintain power for the router and sync module, such as a uninterruptible power supply, then you could power the camera from that too.
Why do you think you might lose power to the camera, and not the other devices?
On this basis, even though you can leave the batteries in, why would you. Not sure why I have either, lol.
Why Blink support would have advised against this, when it has been stated so clearly, so many times, by Blink, I can only put down to incompetence.