

Yep, they would need both fighters and AEW&C to make AEW&C effective. But if they at least have more modern jets, deploy their anti-air defenses strategically and use radar tricks to hit F-35 then they would be able to tick the scales a bit. But this depends on how much Iranian air forces are used to these tactics and are used to the more modern equipment.
The US will never admit their F-35 got shot. They alleged a few F-35 fell into the ocean after defensive maneuvers done by a carrier. Note that this happened at least twice.