Does closure of US, UK and French embassies in Yemen signal Iran/Saudi War?

On Tuesday it was reported that the US, UK and French embassies were being closed and their citizens were ordered to leave Yemen as soon as possible.
This comes after a Shiite coup, believed to be backed by Iran, overthrew the Sunni Saudi-backed government.

The US embassy in Yemen is the third to close in the Middle East since the closure of embassies in Tripoli, Libya and in Damascus, Syria. This looks set to have severe consequences for the separate drone programs of both the CIA and Joint Special Operations Command with the co-operation of the previous government who involved in targeting and killing al-Qaida in the Arabian Peninsula members in the Yemen.

The fall of Yemen on the south east corner of the Arabian peninsula means that a pro-Iranian government could potentially harass shipping from the Mediterranean to the Indian Ocean via the Suez Canal and the Red Sea while the Persian Gulf could be threatened by a pro-Iranian Shia government in Iraq and by Iran itself which menaces Saudi Arabia from across the Persian Gulf. To the north Saudi Arabia borders Iraq and Syria where ISIS also threatened. Across the Red Sea there is no love lost by the Egyptian military toward Saudi Arabia who backed the Sunni Muslim Brotherhood regime which was recently toppled by a coup.

With America apparently in retreat on every front and soon to withdraw from Afghanistan which also borders Iran, it would appear that Saudi Arabia is becoming increasingly isolated. Could this weakness encourage Iran to tighten the screws? Iran has close ties to Russia who resent the glut in oil production by the Saudis which has led to the recent slump in Russia's oil prices and both Iran and Russia support Bashar Assad who is fighting against Sunni insurgents backed by the Saudis. Iran is getting close to having a nuclear weapon while rumors abound that the Saudis have a secret nuclear program to build a bomb of their own.

The Arab Spring has led to the destabilization of the majority of Sunni Muslim states across the Middle East. This process was backed by the Saudis who want to see the end of secular dictatorships that blocked the rise of Islamic states that could become under the umbrella of a Saudi led Islamic Caliphate. The rise of ISIS means they have lost control of their Frankenstein monster and the Saudis fear an internal revolt from returning Saudi Islamic extremists spurred on by success abroad.

Iran's seizure of Yemen with the use of Shiite Houthis rebels aided by Hezbollah fighters mimics their strategy in Lebanon whereby a pro-Iranian Hezbollah state has been set up in the south of the country.

Could the Saudi house of cards come crashing down if the Iranians blow a bit stronger?