Hardwire spotlight cam to outlet

I have a few outlets under the soffit around my house. I'd like to avoid plugging the cams into the outlet for a couple reasons. First the outlets are switched so don't want the possibility of someone turning these outlets off. Second I would rather not have the opportunity for someone to unplug the camera. My thoughts are that I could run the power wire from the camera and hardware it directly to the always hot wire in the outlet and the neutral and ground in the outlet. is this a possible supports configuration? Can I some how run romex from the camera to the outlet?