Frankly I'm not sure they could dislodge Iraq from Kuwait. The RSAF was competent enough to seriously degrade any Iraqi attempt to invade Saudi, and I'm sure that a combined Gulf/Saudi/Egyptian/Syrian(??) force could stop the Iraqis inside the Saudi border, but anything past that....
I hate to bring out the old stereotypes, but the classic Arab disunity and military disorganization would come out in force. Even OTL organizing a multinational force to re-take Kuwait was a colossal undertaking, and that was with a majority NATO force which had been training together for years. Remember, 1991 is when "friendly fire" entered popular vernacular. Now imagine it with Saudis, Omanis, Bahrainis, Emiratis, and who knows what other Arab forces, all speaking ostensibly the same language in mutually unintelligible dialects, all somewhat resentfully under, say, a Saudi command which has never run or even thought of an operation this big.....
The Gulf States would be comfortable being under Saudi command, but there would be huge rivalries in any larger Arab coalition....either Egypt or Syria would be in it, but probably not both, and Egypt would probably view itself as rightful head of the coalition. The most competent army in the Arab world- the Jordanian- would sit out the war for political reasons, and I think it would wind up being a Saudi+Gulf state+ token other Arab effort...which doesn't bode well for it's military effectiveness. Several of the Gulf state forces are essentially mercenary armies staffed by Pakistani soldiers from the Punjab. The most effective gulf force, Oman, is too small to make a dent in the Iraqi army. The Saudi land forces are judged by outside observers to be essentially a military non-entity despite their equipment.
That being said, an ATL battle of Kafji with an Iraqi probe repulsed by Gulf troops, followed by a pan-Arab bombing campaign led by the competent RSAF against (southern) Iraq and occupied Kuwait would probably be the extent of things before a political solution was found.
Now, get ready for that battalion-sized ATL Kafji action to become the next battle of Badr after the war......