My idea of a formula:
Ships Power cap: 200mil
Ships mass: 200k
Ships Thrust 150k
((Mass/PowerCap)*(Mass/Thrust))*1000=1.33=Time to shutdown/start up
Prehaps the actual formula could involve shields and all this, but my example here is to base it off of the ships weight and the systems amount, or prehaps their power cost.
In this example, on that formula, it will take you 80 seconds to shut your ship down and 80 to start it back up. This will balance things like using them like you would a radar jammer or cloaker, to hide during combat.
This "Offline Mode" could also allow stations systems to work on it. Plex lifters (idk, are they added already?), Undeathinators could be working when the ship is offline, same with factory systems.
Prehaps there could be a hidden offline and a stationary offline.
The hidden would shut down everything like you said to hide you, while stationary would just shut down thrusters for prehaps a boost in power generation, shield regen (maybe lose the % loss that you get while in combat), and allow station systems to work.
EDIT: Prehaps you could make them trackable only by a special scanner that detects hulls, so a ship with no hulls would be a little brighter than a space black ship, but would be harder to detect if your not truly looking for them. The same with the current scanner system can just be system scan, and because every ship has a core, it can detect any active ship.