If your docked thing with thrusters is a simple engine pod, you won't need to have a reactor in it, because that reactor would be forced into an inactive state, and the engine pod will instead use power from the structure it's docked on... at least when you throttle them up (same as if those thrusters would be built onto the main structure).
But in case you have something like a fighter with its own thrusters docked to a carrier ship, you can still use the "Inherit thrust" option... The fighter will have its reactor disabled while it's docked, and the carrier will inherit extra thrust and power load from it, and when you undock the fighter, its own internal power source will turn on automatically, so you'll have to have one in it.
The rule is that, no matter how many layers of stacked docked stuff you have in a so-called "docking chain", you can only pilot the base structure (called the "mother entity"). And only the mother entity can have an
active reactor and active shield, so it's the source of all power and shielding for everything that's docked upon it. So only stuff that you intend to undock and use on their own need to have their own systems.
And yes, when things are docked, only those blocks on them are protected which are within the mother entity's shield bubble.
Whoops, this got a little long... sometimes I get carried away when wording stuff that I learned through experimentation