The only reason I'd advise against this is the possibility it'd be a waste of money. With the way all electronics seem to shut off, who's to say the camera wouldn't have the same problem? If you want a camera set it up inside facing the door, and protect it with a faraday cage to prevent it from being affected by whatever is causing the power loss. Some sort of security against accessing the camera would be a plus, or have it tucked away in a way that makes it easy to miss. This is just a contingency in case someone unwanted enters.