Yes, sectors don't have fleets and don't do any research on their own.
But you can build armies, defensive or otherwise, on them?You can build stuff within your sectors as you would be able to if they were a part of your core worlds, yes. Space ports are not off limits (if I recall correctly), however you may not manage planet surfaces or construct new buildings on planets, that stuff is left to the AI in charge of the sector.
You can hear Wiz discuss it on one of the episodes of the ETT stream, specifically here. It is discussed more in later streams too, so I'd definitely suggest giving them a watch (or listen) over time.
Well, technically they do have research (in the sense that they produce research - it all goes to the empire's chosen technological progression) and do have fleets (just only constructor ships for them to build improvements with).
But yes, all military installations are under your control in both the core worlds and sectors, afaik.
But you can build armies, defensive or otherwise, on them?