I concur with LW's assessment that Iran will find a way to get hold of nuclear weapons. If anything current nastiness will be an added motivation. They see their lack of a nuclear deterrent as an existential threat and would love to be in the same position as N Korea.
In some ways, the Saudis already have nukes. They are believed to have financed the Pakistani programme and the quid pro you had culminated in the Saudi/Pakistan defence pact with its NATO Article 5 equivalent.