Wars are fought and determined on the ground. Air force is only a tactical advantage over your foe to help you achieve these:
1.
Attack enemy's military and vital infrastructure to deactivate their command structure, communication, power generation and transportation.
Iran's missile arsenal can achieve this objective without any problem. While I seriously doubt GCC's AF could inflict the same damage without considerable loss of their own jets due to Iran's advanced air defense system and strategic depth. Whole GCC countries are easily within reach of Iran's missiles. So Iran doesn't really need any air force.
2. Air support for their naval forces:
First GCC doesn't posses any potent naval force to begin with and second, Iran's ASHBM and Cruise missile arsenal can easily inflict a significant damage to them. I will leave out Iran's submarines and fast attack ships out of it. So again, Iran doesn't need any air force.
3. Support their ground forces:
GCC countries don't have shared land border with Iran. They only have two ways to get their ground forces to Iran. One is through the sea which is a long shot given Iran's missiles and naval supremacy. 2nd is through Irag's lands which is not going to happen unless GCC declare war on Iraq too which then it will have bigger problems. So again I don't see any use for GCC's airforce here.
So overall, I know most of you are counting on a dog fight style confrontation between Iran's and GCC air force in a war scenario but it is not going to happen. Iran is not going to even fly a single jet fighter in the first few days of the battle. Instead, it is going to fly hundreds of missiles hitting airports, refineries, ports, power and desalination plants. After it made sure no runway is left for GCC airforce to fly its jets, It will sweep all GCC naval units in Persian Gulf using its submarines and fast attack boats and blockade their ports. And if GCC countries have not returned to their senses by then, it will start a seaborn ground force invasion. But I doubt it ever get to that point.