I don't doubt we would dominate the air...I wonder whether we could hold ground. All the air dominance in the world is worthless if there is a hostile tank on your runway and a squad in the control tower.
In order to take ground you have to be able to maneuver, if someone else dominates the air you can't maneuver. Holding ground you already own is a different matter (that's why air power is no substitute for invasion in offensive operations). Whatever force the new saudi regime would put against us would not be able to move and its' supply lines would be completely destroyed. No way would any saudi soldiers get anywhere close to our bases (or those of our allies).
The Saudi Army is fairly well equipped. But it is small. And its competence is rather questionable. And most of their equipment comes from us. Remember the problems we caused for Iraq in 91 with computer equipment with hidden backdoors and viruses? You can be sure that we have such in what we have sold to the Saudis... And to add to the picture, I have no doubt that much like the Jihadis, we have hordes of informers within the ranks.
The Saudi military just isn't a threat to us. Their wealth is. KSA fully in the Osama camp would have more then enough cash to make AQ a nuclear power...