Yes, you can create a docker image of your product and publish it to a docker registry. Your customers can then pull the image from there and fire up containers. Docker.io doesn't offer private images yet, so you may want to run your own registry [1] if you need to restrict access.
Docker doesn't let you push updates to containers. I think the best you can do is to push a new image to your registry and ask your customers to pull and fire up new containers.