So I usually play single player, but worry the insurgency will spread too quickly and become uncontrollable. My question is, do friendly AI remove installations when the come across one or capture a town?

I typically play singleplayer myself, and I try to be a little more conservative where I put my forces for insurgencies and the amount of pre-placed installations. For example, I will either manually place my units around the map in small crevices of the map or use custom objectives to spawn them, and then use civ and mil placement modules as "objective only" tasks for the OPCOM, that way it will take a little bit for the insurgency to spread. I'll typically keep the pre-placed installation level to none or low, as well.

Though virtualized AI cannot really detect/do anything with installations, I set up triggers using AI under HC control to call out in sidechat whenever they come across an installation. It makes it nice when AI can help sweep villages.