You can!
I do not own the Ford Truck or the Camaro Xfinity stock cars, but I still painted the black/yellow Cam Waters truck and the blue SVG Wendys car.
You can preview your livery in the store section of the UI, the same way you do in the My Content section. Just name your paint as you normally would (i.e. car_num_613857.tga) in the correct folder and it comes up.
To see the cars in action on a track, just upload it to Trading Paints and make an AI carset for yourself. That's how I got those
action shots. Set up a race against the AI and pick Charlotte oval as the venue. The cars will grid up on that angle behind the pace car.