Is it possible for me to set up an insurgency mission against an occupying force? For example playing guerrilla against CSAT or something like that?
Yes you can, but as far as I'm aware, you won't really be able to participate in the building of IED factories, civ recruitment centers, etc. Also, bare in mind, AI can't destroy these HQ's like players can, so in all likelihood they will just keep forming and forming until you overwhelmed the non-insurgent side.
If you were to try this, I'd use a high value for the civ recruitment minimum civs present option (in the Commander module for the Assymetric side, default value is 2), that way you don't keep getting new groups constantly.