I'm confused. Why would you use an engineless ship over a satellite for this? The sat would have many advantages: could be built at any planet - not tying up a spaceyard, no maintenance, cheaper to build, can't be captured, etc.
The one advantage I can guess is that the ship will immediately be in space. A satellite will be cheaper and easier to make,but you still need to launch it once it is built, and that takes another turn. Perhaps its urgent that you detect cloaked vessels the next turn. Apart from that its just an intellectual question ie. although we would never do it, would it work if indeed we did do it for some reason.
Not intellectual. A ship with no engines can be built in one turn on emergency built on a colony world. Rather than waiting two turns. I need static scanners anyway.
And it wouldn't be a starbase, it would be an escort.