Not necessarily- look up Cargo Cult. On some islands during WWII, the natives saw the planes landing at US bases and offloading all their cargo. Because the natives didn't understand large scale manufacturing and shipping, they thought the planes were delivering the cargo from the gods. That the US had actually conned the gods into giving the natives' share to the US troops. So the natives built their own airstrips and control towers (from native materials - they thought the towers were alters, so it was the form that mattered. Then they waited for their share of the gods' cargo to be delivered to them.
Bottom line - those who are ignorant, whether willfully or otherwise, will find ways to rationalize their viewpoints. Start using space travel for shipping, travel, and tourism and the conspiracy theorists will simply adjust their conspiracies to either encompass the new information or rationalize it into their pet theories. No matter WHAT evidence you might present, their theories are right and you are just part of the conspiracy.
Good point. I guess even if you took them into space and showed them the earth, they could claim that they were brainwashed and mind-controlled. You're right. There is no such thing as educating the irrational.