Not a chance. Lets look at some facts.
1. KSA don't have the manpower to win a war in Yemen, against Iranian backed rebels.
2. KSA asked America to defend it against Iran.
3. KSA remained silent against a recent drone based bombing of oil fields, although it blamed Iran.
4. KSA has a significant shia population. There will be enough amongst them, loyal to Iran due to religious afilliations to create an insurgency in Saudi if they sided with Iran.
Iran has a huge landmass. Take a look at this;
That's 4 times the land mass of Iraq. Imagine the force required to keep a hold of that territory. Also it's mostly mountains, think to how difficult moving in Afghanistan is for NATO forces.