If it's bookmarked in the browser, then the browser will try and connect and then fail and no real way for the system to basically catch that without a major overhaul on how things work (basically open up all the ports, see if a request comes in on such and such port, see if it matches a webURL and then start the container, wait a bit, then redirect to the URL in question)
On the other hand, I can see that the webUI entry in the docker tab being able to start up the container if it's not running, but it might not be worth the programming because since you're there on the docker / dashboard tab anyways, its really not much to start the container and then click the webURL.
Nice idea though.