This came up about 3 months ago -there's a thread somewhere. Several seemed to think the Saudis had a few nukes with their name on tucked away in Pakistani silos. This makes them ready for delivery in a few hours, but allows them to deny having any. Pure speculation, of course
As to the balance of power - it just ensures it if/when the Iranians get nukes (Those Shias & Sunnis, they're just
such good mates), or the Israelis look like threatening the Sauds.