Back about a year ago, when I was looking for an action camera like the GoPro Hero I remember reading that the GoPro Hero will not provide video while the USB power/recharge cable is plugged in. So, it was/is only useable on its internal battery
That is why I bought a Swann's 'GoPro' equivalent. The Swann will capture video with the USB power/recharge cable is plugged in. It also has a removeable LCD screen, which the GoPro did not.
Now, GoPro may have changed that configuration since then, so you'll have to do some research.