I don't think Greek ideas had a whole lot to do with the development of western civillization because I don't think anyone really knew what they were. I think they were mostly forgotten until recent history.
My first degree is in astronomy. It has always surprised me that by 200 BC the Greeks knew that the Earth, Moon, and the Sun were spheres, that the Moon orbited the Earth and the Earth went around the Sun and they even knew the sizes of the Earth, Sun, and Moon, and the distance from the Earth to the Moon and the distance from the Earth to the Sun.
They figured this all out just using simple geometry and common sence. They had a hard time figuring out the diameter of the Earth (which was the unit of measure in all of the distance calculations) but they got a lucky break when one day when a Greek in Egypt discovered a well in Egypt that had no shadow, it was pointing straight at the sun.
The only reason the Greeks could not come up with an accurate model of the solar system was because they hadn't "discovered" ellipses. They figured heavenly bodies just had to move in circles.
Ptolemy's model of the solar system had the planets and the sun moving in circles, and the focuses of these circles moved around the Earth in circles. This created the zig zag effect where planets go one way in the sky then turn around and go back the other way before turning around again. I don't believe he ever tried to claim this was how the solar system was laid out, because that would have contradicted early observations, it was just a mathematical model that worked to predict where a planet would be in the sky at a certain point in time.
So then western society seems to have cast out all of this information, took Ptolemy's model minus the mini-orbits and said that was the way things were, which is amazingly ignorent.
I just find it weird that when Columbus was sailing off, people were telling him the world was flat and he would fall off the edge of the earth. Also, he had no idea how far he would have to go to hit the orient.
1700 years before he departed, the Greeks could have told him exactly how many miles (well they would have used stadia) he would have to travel to hit the orient.
Anyway, my point is that if Greek scientific discoveries were so twisted and forgotten so that they ended up being used to promote ignorence in society, I would bet Greek democratic ideas suffered the same fate.
I don't know, but I would guess Greek philosophers were used to justify monarchies and the church, and were probably seen by reformers as part of the problem rather than the solution.