I think that would be a rather boring way to play.
You got mines that mines units of resources that have to be picked up (300 gold and 400 steel) and brought to a spaceport, which can use them to build ships. This makes the universe alive with traffic that you don't control, at least not directly.
A single ship means rather little in this game, apart from certain alien design ships (advanced) that can appear randomly in the early game.
To mimic a single ship, automate everything, but take one ship for yourself. You can always remove automation for single ships or fleets. A single fleet would probably work better, especially if you tailor it yourself and make it strong. I have had fun with only controlling the military ships. The catch back then (and probably still) is that the automatic diplomacy AI is not very informative about changes in war status.
Many new players dislike lots of automation early on, as it may feel like the game playing itself. You have to figure out what works for you.
Since I have not played CK2 I can't compare on its background simulation. DW got an entertaining galaxy that is alive, it is quite possible to make something more complex. I am not too keen on picking up CK2, since it is never really cheap, and I doubt that I would be willing to invest enough time to really enjoy it.