More interesting would be if compnonents that use static energy cease to function (like recreation centers and so on) Maybe i will have a look into that in the future.
It would seem that "semi-active" components (I've tested Construction Yards + Manufacturing Plants, Energy Labs, Gas Extractors) do not need energy to function. They seem, however, to still use energy if any is available (you can see fuel being burned).
It would seem that you can, for instance, design a gas mining station (with no shields, weapons or energy collectors) with the reactor and fuel cell components in the last order of being built, cancel the construction just before they are built, and the station will function without any problems (saving you fuel and some resources in the process). (There is, however a consequence if you cancel early : the construction ship will not drop the extra resources the station might need for retrofitting, so your freighters will have to waste some time bringing them in (or other freighters, where this might cost you some money).)
About the energy collectors :
Maybe the formula for energy collectors collection rate in systems (black hole and gas clouds excepted) is :
where scaling_factor seems to be about 0.125(+/-0.025) considering that I saw several Red Giants have 90 total energy and several main sequence stars have 70 total energy?