Sounds like a "querilla" or insurgent force. Well in 2008 a NATO country in Iraq would probably be fighting insurgents together with the regular Iraqi army. I've read somewhere that for U.S., Brits etc the picklist would select insurgent forces as their opponents for a "current" battle but can't pinpoint the post right now.
Correct - post the 2003 invasion when the Iraqi regular army was destroyed, then the AI pick list will pick for the current insurgents to give the appropriate OPFOR to the coalition forces (to include playing as the US-supplied Iraqi govt forces).
Playing with a squillion points core against these is therefore not a good idea, unless you really like to see a tide of humanity, since they have no heavy equipment to soak up the points. Just like any other guerilla army.
Try 2-3K points of coalition forces at most. They are really not meant for a campaign, but for use in building scenarios. Not unless you maybe restrict yourself to a low-points core based on a rifle company (with attachments) doing anti-insurgency patrols.