A:Answer Yes to charging but no to hard-wire; as long as you have USB charging on your bike, you can use the camera while charging. I have a USB attachment that is hard wired to my battery. The waterproof cap disables power when the ports are covered so your battery doesn’t drain.
Another option is to mod your helmet, if it’s attached there, to include a cheap USB battery for longer trips. I have a friend who did that but with light strips and it works great. Just find something that’ll work for you.